Question 1

Solve the problem.
-$$\left\{ \begin{array} { r } 
x - 7 y = - 1 \
2 x - 6 y = - 2
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 1 , - 1 ) \}$ 
B)  $\{ ( 0 , - 1 ) \}$ 
C)  no solution; $\varnothing$ 
D)  $\{ ( - 1,0 ) \}$ 
A)  $\{ ( 1 , - 1 ) \}$ 
B)  $\{ ( 0 , - 1 ) \}$ 
C)  no solution; $\varnothing$ 
D)  $\{ ( - 1,0 ) \}$

Question 2

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { l } 
( - 3,4,1 ) \
3 x + 3 y + z = 4 \
4 x - 4 y - z = - 29 \
2 x + y + 4 z = 2
\end{array} \right.$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 3

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( 0,2 , - 5 ) \
\left\{ \begin{aligned}
x - y + 3 z & = - 17 \
2 x + z & = - 5 \
x + 2 y + z & = - 1
\end{aligned} \right.
\end{array}$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 4

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { l } 
( 4,5 , - 1 ) \
3 x + 3 y + z = 16 \
5 x - 4 y - z = - 29 \
3 x + y + 5 z = 22
\end{array} \right.$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 5

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
-$$\left\{ \begin{array} { l } 
2 x + y = 3 \
2 x + y = 2
\end{array} \right.$$

Accepted Answer

A)  no solution; $\varnothing$ 
B)  $\left\{ \left[ \frac { 3 } { 2 } , 0 \right) \right\}$ 
C)  infinitely many solutions; $\{ ( x , y ) \mid 2 x + y = 3 \}$ or $\{ ( x , y ) \mid 2 x + y = 2 \}$ 
D)  $\{ ( 1,0 ) \}$ 
A)  no solution; $\varnothing$ 
B)  $\left\{ \left[ \frac { 3 } { 2 } , 0 \right) \right\}$ 
C)  infinitely many solutions; $\{ ( x , y ) \mid 2 x + y = 3 \}$ or $\{ ( x , y ) \mid 2 x + y = 2 \}$ 
D)  $\{ ( 1,0 ) \}$

Question 6

Solve the problem.
-$$\left\{ \begin{array} { l } 
y - 6 x = 4 \
4 y = 24 x + 16 \
\text { A) } \{ ( - 1.5 , - 1 )
\end{array} \right.$$

Accepted Answer

A)  $\{ ( - 1.5 , - 1 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 1,1 ) \}$ 
D)  infinitely many solutions; $\{ ( x , y ) \mid y - 6 x = 4 \}$ or $\{ ( x , y ) \mid 4 y = 24 x + 16 \}$ 
A)  $\{ ( - 1.5 , - 1 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 1,1 ) \}$ 
D)  infinitely many solutions; $\{ ( x , y ) \mid y - 6 x = 4 \}$ or $\{ ( x , y ) \mid 4 y = 24 x + 16 \}$

Question 7

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
-$$\left\{ \begin{array} { l } 
3 x + y = - 11 \
4 x + 2 y = - 12
\end{array} \right.$$

Accepted Answer

A)  {(-3, -2)} 
B)  {(-5, -6)} 
C)  {(5, 4)} 
D)  {(-5, 4)} 
A)  {(-3, -2)} 
B)  {(-5, -6)} 
C)  {(5, 4)} 
D)  {(-5, 4)}

Question 8

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
-$$\left\{ \begin{array} { l } 
\frac { 1 } { 3 } x + \frac { 1 } { 3 } y = 1 \
\frac { 1 } { 4 } x - \frac { 1 } { 4 } y = - \frac { 9 } { 4 }
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 3,7 ) \}$ 
B)  $\{ ( - 3,6 ) \}$ 
C)  $\{ ( - 4,7 ) \}$ 
D)  no solution; $\varnothing$ 
A)  $\{ ( 3,7 ) \}$ 
B)  $\{ ( - 3,6 ) \}$ 
C)  $\{ ( - 4,7 ) \}$ 
D)  no solution; $\varnothing$

Question 9

Determine whether the ordered pair is a solution of the system.
-(-2, -1) $$\left\{ \begin{array} { l } 
2 \mathrm { x } = 3 - \mathrm { y } \
4 \mathrm { x } = 6 - 2 \mathrm { y }
\end{array} \right.$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 10

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
-$\left\{\begin{array}{l}
y-4 x=2 \
6 y=24 x+12
\end{array}\right.$

Accepted Answer

A)  $\{ ( 1,1 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( - 1.5 , - 1 ) \}$ 
D)  infinitely many solutions; $\{ ( x , y ) \mid y - 4 x = 2 \}$ or $\{ ( x , y ) \mid 6 y = 24 x + 12 \}$ 
A)  $\{ ( 1,1 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( - 1.5 , - 1 ) \}$ 
D)  infinitely many solutions; $\{ ( x , y ) \mid y - 4 x = 2 \}$ or $\{ ( x , y ) \mid 6 y = 24 x + 12 \}$

Question 11

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
-$$\left\{ \begin{array} { l } 
4 x + 4 y = 36 \
2 x - 2 y = 2
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 5,4 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 4 , - 6 ) \}$ 
D)  $\{ ( 4,5 ) \}$ 
A)  $\{ ( 5,4 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 4 , - 6 ) \}$ 
D)  $\{ ( 4,5 ) \}$

Question 12

Solve the problem.
-The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $11 per
Pound. How many pounds of the $6 coffee should be used?

Accepted Answer

A)  72 pounds 
B)  144 pounds 
C)  27 pounds 
D)  54 pounds 
A)  72 pounds 
B)  144 pounds 
C)  27 pounds 
D)  54 pounds

Question 13

Solve the problem.
-An electronics company kept comparative statistics on two products, A and B. For the years 2003 to 2011, the total number of Product A ever sold (in thousands) is given by the equation y = 77x + 200, where x is the
Number of years since 2003. For that same period, the total number of Product B ever sold (in thousands) is
Given by the equation y = -30x + 434, where x is the number of years since 2003. Use the substitution method to
Solve the system and choose the statement that most accurately describes the solution.

Accepted Answer

A)  At about 2.2 years (to the nearest tenth) since 2003, the company sold the same number of Product A as Product B. 
B)  At some point between 2003 and 2011, the company had sold 2200 of each product. 
C)  When 369,000 of Product A had been sold, 2.2 times as many of Product B had been sold. 
D)  The company sold about 2.2 times as many of Product B as Product A. 
A)  At about 2.2 years (to the nearest tenth) since 2003, the company sold the same number of Product A as Product B. 
B)  At some point between 2003 and 2011, the company had sold 2200 of each product. 
C)  When 369,000 of Product A had been sold, 2.2 times as many of Product B had been sold. 
D)  The company sold about 2.2 times as many of Product B as Product A.

Question 14

Solve the problem.
-Julie and Eric row their boat (at a constant speed) 16 miles downstream for 2 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the current.

Accepted Answer

A)  5 mph 
B)  3 mph 
C)  2.5 mph 
D)  4 mph 
A)  5 mph 
B)  3 mph 
C)  2.5 mph 
D)  4 mph

Question 15

Solve the problem.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of potato chips for $6.25. Another customer buys 3 hot dogs and 5 bags of potato chips for $9.75. Find the cost of each item.

Accepted Answer

A)  $2.25 for a hot dog; $1.00 for a bag of potato chips 
B)  $0.75 for a hot dog; $2.00 for a bag of potato chips 
C)  $2.00 for a hot dog; $1.00 for a bag of potato chips 
D)  $2.00 for a hot dog; $0.75 for a bag of potato chips 
A)  $2.25 for a hot dog; $1.00 for a bag of potato chips 
B)  $0.75 for a hot dog; $2.00 for a bag of potato chips 
C)  $2.00 for a hot dog; $1.00 for a bag of potato chips 
D)  $2.00 for a hot dog; $0.75 for a bag of potato chips

Question 16

Solve the problem.
-$$\left\{ \begin{array} { l } 
y = 1.4 x - 3.7 \
y = 0.8 x - 3.04
\end{array} \right.$$

Accepted Answer

A)  $\{ ( - 1.1 , - 2.16 ) \}$ 
B)  infinitely many solutions; $\{ ( x , y ) \mid y = 1.4 x - 3.7 \}$ or $\{ ( x , y ) \mid y = 0.8 x - 3.04 \}$ 
C)  no solution; $\varnothing$ 
D)  $\{ ( 1.1 , - 2.16 ) \}$ 
A)  $\{ ( - 1.1 , - 2.16 ) \}$ 
B)  infinitely many solutions; $\{ ( x , y ) \mid y = 1.4 x - 3.7 \}$ or $\{ ( x , y ) \mid y = 0.8 x - 3.04 \}$ 
C)  no solution; $\varnothing$ 
D)  $\{ ( 1.1 , - 2.16 ) \}$

Question 17

Solve the system by the best method. Use set notation to express the solution set.
-$$\left\{ \begin{array} { l } 
- 2 x - 8 y = - 38 \
6 x - 9 y = - 18
\end{array} \right.$$

Accepted Answer

A)  $\{ ( - 3,5 ) \}$ 
B)  $\{ ( 3,4 ) \}$ 
C)  $\{ ( 2,5 ) \}$ 
D)  no solution; $\varnothing$ 
A)  $\{ ( - 3,5 ) \}$ 
B)  $\{ ( 3,4 ) \}$ 
C)  $\{ ( 2,5 ) \}$ 
D)  no solution; $\varnothing$

Question 18

Solve the problem.
-$$\left\{ \begin{array} { l } 
9 x + 4 y = 20 \
- 2 x - 2 y = - 10
\end{array} \right.$$

Accepted Answer

A)  $\{ ( - 1,6 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 0,6 ) \}$ 
D)  $\{ ( 0,5 ) \}$ 
A)  $\{ ( - 1,6 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 0,6 ) \}$ 
D)  $\{ ( 0,5 ) \}$

Question 19

Solve the problem.
-A barge takes 2 hours to move (at a constant rate) downstream for 16 miles, helped by a current of 3 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)  5 hours 
B)  32 hours 
C)  8 hours 
D)  2 hours 
A)  5 hours 
B)  32 hours 
C)  8 hours 
D)  2 hours

Question 20

Solve the system by the best method. Use set notation to express the solution set.
-$$\left\{ \begin{array} { l } 
3 x = - 9 \
x + 5 y = 17
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 3,4 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 3 , - 4 ) \}$ 
D)  $\{ ( - 3,4 ) \}$ 
A)  $\{ ( 3,4 ) \}$ 
B)  no solution; $\varnothing$ 
C)  $\{ ( 3 , - 4 ) \}$ 
D)  $\{ ( - 3,4 ) \}$

Solve the problem. - $\left\{ \begin{array} { r } x - 7 y = - 1 \\2 x - 6 y = - 2\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } ( - 3,4,1 ) \\3 x + 3 y + z = 4 \\4 x - 4 y - z = - 29 \\2 x + y + 4 z = 2\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - (0,2,-5) x-y+3z =-17 2x+z =-5 x+2y+z =-1

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } ( 4,5 , - 1 ) \\3 x + 3 y + z = 16 \\5 x - 4 y - z = - 29 \\3 x + y + 5 z = 22\end{array} \right.$

Solve the problem. - $\left\{ \begin{array} { l } y - 6 x = 4 \\4 y = 24 x + 16 \\\text { A) } \{ ( - 1.5 , - 1 )\end{array} \right.$

Determine whether the ordered pair is a solution of the system. -(-2, -1) $\left\{ \begin{array} { l } 2 \mathrm { x } = 3 - \mathrm { y } \\4 \mathrm { x } = 6 - 2 \mathrm { y }\end{array} \right.$

Solve the problem. -The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $11 per Pound. How many pounds of the $6 coffee should be used?

Solve the problem. -Julie and Eric row their boat (at a constant speed) 16 miles downstream for 2 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the current.

Solve the problem. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of potato chips for $6.25. Another customer buys 3 hot dogs and 5 bags of potato chips for $9.75. Find the cost of each item.

Solve the problem. - $\left\{ \begin{array} { l } y = 1.4 x - 3.7 \\y = 0.8 x - 3.04\end{array} \right.$

Solve the system by the best method. Use set notation to express the solution set. - $\left\{ \begin{array} { l } - 2 x - 8 y = - 38 \\6 x - 9 y = - 18\end{array} \right.$

Solve the problem. - $\left\{ \begin{array} { l } 9 x + 4 y = 20 \\- 2 x - 2 y = - 10\end{array} \right.$

Solve the problem. -A barge takes 2 hours to move (at a constant rate) downstream for 16 miles, helped by a current of 3 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.

Solve the system by the best method. Use set notation to express the solution set. - $\left\{ \begin{array} { l } 3 x = - 9 \\x + 5 y = 17\end{array} \right.$

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Basics of Functions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 4: Systems of Linear Equations

Solve the problem. - {x−7y=−12x−6y=−2\left\{ \begin{array} { r } x - 7 y = - 1 \\2 x - 6 y = - 2\end{array} \right.{x−7y=−12x−6y=−2​

Determine if the given ordered triple is a solution of the system. - {(−3,4,1)3x+3y+z=44x−4y−z=−292x+y+4z=2\left\{ \begin{array} { l } ( - 3,4,1 ) \\3 x + 3 y + z = 4 \\4 x - 4 y - z = - 29 \\2 x + y + 4 z = 2\end{array} \right.⎩⎨⎧​(−3,4,1)3x+3y+z=44x−4y−z=−292x+y+4z=2​

Determine if the given ordered triple is a solution of the system. - (0,2,-5) x-y+3z =-17 2x+z =-5 x+2y+z =-1

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - {2x+y=32x+y=2\left\{ \begin{array} { l } 2 x + y = 3 \\2 x + y = 2\end{array} \right.{2x+y=32x+y=2​

Solve the problem. - {y−6x=44y=24x+16 A) {(−1.5,−1)\left\{ \begin{array} { l } y - 6 x = 4 \\4 y = 24 x + 16 \\\text { A) } \{ ( - 1.5 , - 1 )\end{array} \right.⎩⎨⎧​y−6x=44y=24x+16 A) {(−1.5,−1)​

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - {3x+y=−114x+2y=−12\left\{ \begin{array} { l } 3 x + y = - 11 \\4 x + 2 y = - 12\end{array} \right.{3x+y=−114x+2y=−12​

Determine whether the ordered pair is a solution of the system. -(-2, -1) {2x=3−y4x=6−2y\left\{ \begin{array} { l } 2 \mathrm { x } = 3 - \mathrm { y } \\4 \mathrm { x } = 6 - 2 \mathrm { y }\end{array} \right.{2x=3−y4x=6−2y​

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - {y−4x=26y=24x+12\left\{\begin{array}{l}y-4 x=2 \\6 y=24 x+12\end{array}\right.{y−4x=26y=24x+12​

Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express the solution set. - {4x+4y=362x−2y=2\left\{ \begin{array} { l } 4 x + 4 y = 36 \\2 x - 2 y = 2\end{array} \right.{4x+4y=362x−2y=2​