Question 1

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
- 3 x - 7 y = - 1 \
- 7 x - 4 y = 10
\end{array} \right.$

Accepted Answer

A)  $( 2,1 )$ 
B)  $( 2 , - 1 )$ 
C)  $( - 2 , - 1 )$ 
D)  $( - 2,1 )$ 
A)  $( 2,1 )$ 
B)  $( 2 , - 1 )$ 
C)  $( - 2 , - 1 )$ 
D)  $( - 2,1 )$ D

Question 2

Solve the problem by writing and using a system of linear equations.
-A national wildlife refuge in Michigan has 107 thousand more trees than a national wildlife refuge in Ohio. The total number of trees for both is 307 thousand. Find the number of trees for each.

Accepted Answer

A)  Ohio: 100 thousand trees 
B)  Ohio: 107 thousand trees Michigan: 207 thousand trees Michigan: 214 thousand trees 
C)  Ohio: 107 thousand trees 
D)  Ohio: 50 thousand trees Michigan: 200 thousand trees Michigan: 157 thousand trees 
A)  Ohio: 100 thousand trees 
B)  Ohio: 107 thousand trees Michigan: 207 thousand trees Michigan: 214 thousand trees 
C)  Ohio: 107 thousand trees 
D)  Ohio: 50 thousand trees Michigan: 200 thousand trees Michigan: 157 thousand trees A

Question 3

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
- 6 y = x + 4 \
4 x + 5 y = 3
\end{array} \right.$

Accepted Answer

A)  $( - 2,0 )$ 
B)  no solution 
C)  $( 2 , - 1 )$ 
D)  $( 1,0 )$ 
A)  $( - 2,0 )$ 
B)  no solution 
C)  $( 2 , - 1 )$ 
D)  $( 1,0 )$ C

Question 4

If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Accepted Answer

A) True 
 B)False

Question 5

Solve.
-A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 3 bags of potato chips for $\$ 17.75$. Another customer buys 2 hot dogs and 2 bags of potato chips for $\$ 8.50$. Find the cost of each item.

Accepted Answer

A)  $\$ 2.50$ for a hot dog; $\$ 2.00$ for a bag of potato chips 
B)  $\$ 1.75$ for a hot dog; $\$ 2.50$ for a bag of potato chips 
C)  $\$ 2.75$ for a hot dog; $\$ 2.00$ for a bag of potato chips 
D)  $\$ 2.50$ for a hot dog; $\$ 1.75$ for a bag of potato chips 
A)  $\$ 2.50$ for a hot dog; $\$ 2.00$ for a bag of potato chips 
B)  $\$ 1.75$ for a hot dog; $\$ 2.50$ for a bag of potato chips 
C)  $\$ 2.75$ for a hot dog; $\$ 2.00$ for a bag of potato chips 
D)  $\$ 2.50$ for a hot dog; $\$ 1.75$ for a bag of potato chips

Question 6

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
\frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \
8 x = - y
\end{array} \right.$

Accepted Answer

A)  $\left( \frac { 1 } { 2 } , - 4 \right)$ 
B)  $( 2,4 )$ 
C)  $( 0,0 )$ 
D)  $\left( \frac { 1 } { 4 } , - 2 \right)$ 
A)  $\left( \frac { 1 } { 2 } , - 4 \right)$ 
B)  $( 2,4 )$ 
C)  $( 0,0 )$ 
D)  $\left( \frac { 1 } { 4 } , - 2 \right)$

Question 7

Solve the system of equations by graphing.
-$\left\{\begin{array}{l}
x+y=-2 \
x+y=-3
\end{array}\right.$

Accepted Answer

A)  (-5, 3) 
B)  no solution 
C)  (-5, 2) 
D)  (-3, 1) 
A)  (-5, 3) 
B)  no solution 
C)  (-5, 2) 
D)  (-3, 1)

Question 8

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
2 x + y = 8 \
6 x + 3 y = 24
\end{array} \right.$

Accepted Answer

A)  $( 5 , - 2 )$ 
B)  $( 0,8 )$ 
C)  no solution 
D)  infinite number of solutions 
A)  $( 5 , - 2 )$ 
B)  $( 0,8 )$ 
C)  no solution 
D)  infinite number of solutions

Question 9

Without graphing, decide:
(a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
-$\left\{ \begin{aligned}
y - 5 x & = 4 \
5 y & = 25 x + 20
\end{aligned} \right.$

Accepted Answer

A)  lines intersecting at a single point; one solution 
B)  parallel lines; no solution 
C)  identical lines; infinite number of solutions 
A)  lines intersecting at a single point; one solution 
B)  parallel lines; no solution 
C)  identical lines; infinite number of solutions

Question 10

Solve.
-One number is 1 less than a second number. Twice the second number is 10 less than 3 times the first. Find the two numbers.

Accepted Answer

A)  13 and 14 
B)  -13 and -12 
C)  12 and 13 
D)  11 and 12 
A)  13 and 14 
B)  -13 and -12 
C)  12 and 13 
D)  11 and 12

Question 11

Solve.
-Two cars leave a city and head in the same direction. After 5 hours, the faster car is 35 miles ahead of the slower car. The slower car has traveled 245 miles. Find the speeds of the two cars.

Accepted Answer

A)  $51 \mathrm { mph }$ and $58 \mathrm { mph }$ 
B)  $49 \mathrm { mph }$ and $56 \mathrm { mph }$ 
C)  $42 \mathrm { mph }$ and $49 \mathrm { mph }$ 
D)  $70 \mathrm { mph }$ and $77 \mathrm { mph }$ 
A)  $51 \mathrm { mph }$ and $58 \mathrm { mph }$ 
B)  $49 \mathrm { mph }$ and $56 \mathrm { mph }$ 
C)  $42 \mathrm { mph }$ and $49 \mathrm { mph }$ 
D)  $70 \mathrm { mph }$ and $77 \mathrm { mph }$

Question 12

Solve the system of equations by graphing.
-$\left\{ \begin{array} { l } 
x + y = 1 \
x - y = - 3
\end{array} \right.$

Accepted Answer

A)  (2, -1) 
B)  no solution 
C)  (-1, 2) 
D)  (-1, -2) 
A)  (2, -1) 
B)  no solution 
C)  (-1, 2) 
D)  (-1, -2)

Question 13

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores.  
-Approximately how many more stores did General have than Acme in 2011?

Accepted Answer

A)  approximately 200 
B)  approximately 250 
C)  approximately 750 
D)  approximately 500 
A)  approximately 200 
B)  approximately 250 
C)  approximately 750 
D)  approximately 500

Question 14

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
\frac { 1 } { 6 } x - 2 y = 1 \
x - 12 y = 6
\end{array} \right.$

Accepted Answer

A)  $( 1 , - 6 )$ 
B)  no solution 
C)  $( 6 , - 1 )$ 
D)  infinite number of solutions 
A)  $( 1 , - 6 )$ 
B)  no solution 
C)  $( 6 , - 1 )$ 
D)  infinite number of solutions

Question 15

Solve.
-A barge takes 6 hours to move (at a constant rate) downstream for 60 miles, helped by a current of 2 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.

Accepted Answer

A)  8 hours 
B)  6 hours 
C)  120 hours 
D)  10 hours 
A)  8 hours 
B)  6 hours 
C)  120 hours 
D)  10 hours

Question 16

Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions.
-Aviva has a total of 70 coins, all of which are either dimes or nickels. The total value of the coins is \$5.95. Find the number of each type of coin.

Accepted Answer

A)  26 nickels; 44 dimes 
B)  21 nickels; 49 dimes 
C)  23 nickels; 47 dimes 
D)  49 nickels; 21 dimes 
A)  26 nickels; 44 dimes 
B)  21 nickels; 49 dimes 
C)  23 nickels; 47 dimes 
D)  49 nickels; 21 dimes

Question 17

Solve the system of equations by either the addition method or the substitution method.
-$\left\{ \begin{array} { l } 
x = - 6 y + 37 \
- 7 x + 5 y = 70
\end{array} \right.$

Accepted Answer

A)  no solution 
B)  $( 5,8 )$ 
C)  $( - 6,8 )$ 
D)  $( - 5,7 )$ 
A)  no solution 
B)  $( 5,8 )$ 
C)  $( - 6,8 )$ 
D)  $( - 5,7 )$

Question 18

Solve.
-Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was $\$ 228$. The cost of a child's ticket was $\$ 7$ less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Accepted Answer

A)  adult's ticket: $\$ 23$; child's ticket: $\$ 16$ 
B)  adult's ticket: $\$ 22$; child's ticket: $\$ 15$ 
C)  adult's ticket: $\$ 21$; child's ticket: $\$ 14$ 
D)  adult's ticket: $\$ 24$; child's ticket: \$17 
A)  adult's ticket: $\$ 23$; child's ticket: $\$ 16$ 
B)  adult's ticket: $\$ 22$; child's ticket: $\$ 15$ 
C)  adult's ticket: $\$ 21$; child's ticket: $\$ 14$ 
D)  adult's ticket: $\$ 24$; child's ticket: \$17

Question 19

Solve the system of equations by the addition method.
-$\left\{ \begin{array} { l } 
x + y = 0 \
x - y = 14
\end{array} \right.$

Accepted Answer

A)  $( 6 , - 6 )$ 
B)  no solution 
C)  $( - 7 , - 6 )$ 
D)  $( 7 , - 7 )$ 
A)  $( 6 , - 6 )$ 
B)  no solution 
C)  $( - 7 , - 6 )$ 
D)  $( 7 , - 7 )$

Question 20

Solve.
-The three angles in a triangle always add up to $180 ^ { \circ }$. If one angle in a triangle is $57 ^ { \circ }$ and the second is 2 times the third, what are the three angles?

Accepted Answer

A)  $57 ^ { \circ } , 82 ^ { \circ } , 41 ^ { \circ }$ 
B)  $57 ^ { \circ } , 83 ^ { \circ } , 40 ^ { \circ }$ 
C)  $57 ^ { \circ } , 80 ^ { \circ } , 43 ^ { \circ }$ 
D)  $57 ^ { \circ } , 81 ^ { \circ } , 42 ^ { \circ }$ 
A)  $57 ^ { \circ } , 82 ^ { \circ } , 41 ^ { \circ }$ 
B)  $57 ^ { \circ } , 83 ^ { \circ } , 40 ^ { \circ }$ 
C)  $57 ^ { \circ } , 80 ^ { \circ } , 43 ^ { \circ }$ 
D)  $57 ^ { \circ } , 81 ^ { \circ } , 42 ^ { \circ }$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } - 3 x - 7 y = - 1 \\- 7 x - 4 y = 10\end{array} \right.$

Solve the problem by writing and using a system of linear equations. -A national wildlife refuge in Michigan has 107 thousand more trees than a national wildlife refuge in Ohio. The total number of trees for both is 307 thousand. Find the number of trees for each.

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 6 y = x + 4 \\4 x + 5 y = 3\end{array} \right.$

If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Solve. -A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 3 bags of potato chips for $\$ 17.75$ . Another customer buys 2 hot dogs and 2 bags of potato chips for $\$ 8.50$ . Find the cost of each item.

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \\8 x = - y\end{array} \right.$

Solve the system of equations by graphing. - $\left\{\begin{array}{l}x+y=-2 \\x+y=-3\end{array}\right.$ $Solve the system of equations by graphing. - \left\{\begin{array}{l} x+y=-2 \\ x+y=-3 \end{array}\right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 2 x + y = 8 \\6 x + 3 y = 24\end{array} \right.$

Without graphing, decide: (a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b) How many solutions does the system have? - $\left\{ \begin{aligned}y - 5 x & = 4 \\5 y & = 25 x + 20\end{aligned} \right.$

Solve. -One number is 1 less than a second number. Twice the second number is 10 less than 3 times the first. Find the two numbers.

Solve. -Two cars leave a city and head in the same direction. After 5 hours, the faster car is 35 miles ahead of the slower car. The slower car has traveled 245 miles. Find the speeds of the two cars.

Solve the system of equations by graphing. - $\left\{ \begin{array} { l } x + y = 1 \\x - y = - 3\end{array} \right.$ $Solve the system of equations by graphing. - \left\{ \begin{array} { l } x + y = 1 \\ x - y = - 3 \end{array} \right.$

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -Approximately how many more stores did General have than Acme in 2011?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { 1 } { 6 } x - 2 y = 1 \\x - 12 y = 6\end{array} \right.$

Solve. -A barge takes 6 hours to move (at a constant rate) downstream for 60 miles, helped by a current of 2 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.

Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. -Aviva has a total of 70 coins, all of which are either dimes or nickels. The total value of the coins is \$5.95. Find the number of each type of coin.

Solve the system of equations by either the addition method or the substitution method. - $\left\{ \begin{array} { l } x = - 6 y + 37 \\- 7 x + 5 y = 70\end{array} \right.$

Solve. -Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was $\$ 228$ . The cost of a child's ticket was $\$ 7$ less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 0 \\x - y = 14\end{array} \right.$

Solve. -The three angles in a triangle always add up to $180 ^ { \circ }$ . If one angle in a triangle is $57 ^ { \circ }$ and the second is 2 times the third, what are the three angles?

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Solving Systems of Linear Equations

Solve the system of equations by the addition method. - {−3x−7y=−1−7x−4y=10\left\{ \begin{array} { l } - 3 x - 7 y = - 1 \\- 7 x - 4 y = 10\end{array} \right.{−3x−7y=−1−7x−4y=10​

Solve the problem by writing and using a system of linear equations. -A national wildlife refuge in Michigan has 107 thousand more trees than a national wildlife refuge in Ohio. The total number of trees for both is 307 thousand. Find the number of trees for each.

Solve the system of equations by the substitution method. - {−6y=x+44x+5y=3\left\{ \begin{array} { l } - 6 y = x + 4 \\4 x + 5 y = 3\end{array} \right.{−6y=x+44x+5y=3​

If the two equations in a system of linear equations are added and the result is 8 = 0, the system has no solution.

Solve. -A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 3 bags of potato chips for $17.75\$ 17.75$17.75 . Another customer buys 2 hot dogs and 2 bags of potato chips for $8.50\$ 8.50$8.50 . Find the cost of each item.

Solve the system of equations by the substitution method. - {12x+2y=−3148x=−y\left\{ \begin{array} { l } \frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \\8 x = - y\end{array} \right.{21​x+2y=−431​8x=−y​

Solve the system of equations by graphing. - {x+y=−2x+y=−3\left\{\begin{array}{l}x+y=-2 \\x+y=-3\end{array}\right.{x+y=−2x+y=−3​

Solve the system of equations by the substitution method. - {2x+y=86x+3y=24\left\{ \begin{array} { l } 2 x + y = 8 \\6 x + 3 y = 24\end{array} \right.{2x+y=86x+3y=24​

Solve. -One number is 1 less than a second number. Twice the second number is 10 less than 3 times the first. Find the two numbers.

Solve. -Two cars leave a city and head in the same direction. After 5 hours, the faster car is 35 miles ahead of the slower car. The slower car has traveled 245 miles. Find the speeds of the two cars.

Solve the system of equations by graphing. - {x+y=1x−y=−3\left\{ \begin{array} { l } x + y = 1 \\x - y = - 3\end{array} \right.{x+y=1x−y=−3​

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -Approximately how many more stores did General have than Acme in 2011?

Solve the system of equations by the substitution method. - {16x−2y=1x−12y=6\left\{ \begin{array} { l } \frac { 1 } { 6 } x - 2 y = 1 \\x - 12 y = 6\end{array} \right.{61​x−2y=1x−12y=6​

Solve. -A barge takes 6 hours to move (at a constant rate) downstream for 60 miles, helped by a current of 2 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.

Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. -Aviva has a total of 70 coins, all of which are either dimes or nickels. The total value of the coins is \$5.95. Find the number of each type of coin.

Solve the system of equations by either the addition method or the substitution method. - {x=−6y+37−7x+5y=70\left\{ \begin{array} { l } x = - 6 y + 37 \\- 7 x + 5 y = 70\end{array} \right.{x=−6y+37−7x+5y=70​

Solve. -Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was $228\$ 228$228 . The cost of a child's ticket was $7\$ 7$7 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Solve the system of equations by the addition method. - {x+y=0x−y=14\left\{ \begin{array} { l } x + y = 0 \\x - y = 14\end{array} \right.{x+y=0x−y=14​

Solve. -The three angles in a triangle always add up to 180∘180 ^ { \circ }180∘ . If one angle in a triangle is 57∘57 ^ { \circ }57∘ and the second is 2 times the third, what are the three angles?

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } - 3 x - 7 y = - 1 \\- 7 x - 4 y = 10\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 6 y = x + 4 \\4 x + 5 y = 3\end{array} \right.$

Solve. -A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 3 bags of potato chips for $\$ 17.75$ . Another customer buys 2 hot dogs and 2 bags of potato chips for $\$ 8.50$ . Find the cost of each item.

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + 2 y = - \frac { 31 } { 4 } \\8 x = - y\end{array} \right.$

Solve the system of equations by graphing. - $\left\{\begin{array}{l}x+y=-2 \\x+y=-3\end{array}\right.$ $Solve the system of equations by graphing. - \left\{\begin{array}{l} x+y=-2 \\ x+y=-3 \end{array}\right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 2 x + y = 8 \\6 x + 3 y = 24\end{array} \right.$

Solve the system of equations by graphing. - $\left\{ \begin{array} { l } x + y = 1 \\x - y = - 3\end{array} \right.$ $Solve the system of equations by graphing. - \left\{ \begin{array} { l } x + y = 1 \\ x - y = - 3 \end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { 1 } { 6 } x - 2 y = 1 \\x - 12 y = 6\end{array} \right.$

Solve the system of equations by either the addition method or the substitution method. - $\left\{ \begin{array} { l } x = - 6 y + 37 \\- 7 x + 5 y = 70\end{array} \right.$

Solve. -Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was $\$ 228$ . The cost of a child's ticket was $\$ 7$ less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = 0 \\x - y = 14\end{array} \right.$

Solve. -The three angles in a triangle always add up to $180 ^ { \circ }$ . If one angle in a triangle is $57 ^ { \circ }$ and the second is 2 times the third, what are the three angles?