Question 1

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $700,000! They agree that Susan should get $50,000 more than Maria, because she gave most of the money. How much will Maria get?

Accepted Answer

A) $280,000 
B) $275,000 
C) $225,000 
D) $325,000 
E) $240,000

Question 2

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $$\left( \begin{array} { c } 
\frac { 1 } { 2 } x - \frac { 1 } { 6 } y = - 12 \
\frac { 1 } { 2 } x + \frac { 1 } { 4 } y = 8
\end{array} \right)$$

Accepted Answer

A) (-10, 46) 
B) (-8, 48) 
C) (-10, 48) 
D) dependent 
E) inconsistent

Question 3

In a mix of pennies and nickels, there are 22 coins with a total value of 82 cents. How many nickels are there?

Accepted Answer

A) 11 nickels 
B) 7 nickels 
C) 8 nickels 
D) 15 nickels

Question 4

The ordered pair (1, 3)is a solution of the given system. $$\left\{ \begin{array} { l } 
2 x + 2 y = 8 \
4 x + 3 y = 13
\end{array} \right.$$

Accepted Answer

A) True 
 B)False

Question 5

Graph the solution of the system: $$\left\{ \begin{array} { l } 
y < 5 x - 3 \
y - 5 x \geq 4
\end{array} \right.$$

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Consider the following system: $$\left\{ \begin{array} { c } 
7 x + y = 54 \
y = - 7 x - 18
\end{array} \right.$$ Substitute $- 7 x - 18$ for y in the first equation. How many variables does the resulting equation contain?

Accepted Answer

A) 1 
B) 0 
C) 2 
D) 4 
E) none of the above

Question 7

Solve the system by graphing. $$\left\{ \begin{array} { l } 
4 x = 4 - 3 y \
4 x + 3 y = 7
\end{array} \right.$$

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Use two equations in two variables to solve the following problem. At a theater, the giant rectangular movie screen has a width $24$ feet less than its length. If its perimeter is $308$ feet, find the area of the screen.

Accepted Answer

A)  $5,669 \mathrm { ft } ^ { 2 }$ 
B)  $5,764 \mathrm { ft } ^ { 2 }$ 
C)  $5,738 \mathrm { ft } ^ { 2 }$ 
D)  $5,873 \mathrm { ft } ^ { 2 }$ 
E)  $5,785 \mathrm { ft } ^ { 2 }$

Question 9

Melodic Music has compact discs on sale for either $15 or $20. If a customer wants to spend at least $60 but no more than $120 on CDs, graph a system of inequalities that will show the possible ways a customer can buy $15 CDs ( x )and $20 CDs ( y ).

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Use the addition method to solve the system. $$\left\{ \begin{array} { c } 
a + b = 5 \
a - b = - 1
\end{array} \right.$$

Accepted Answer

A)  $( 2 , - 3 )$ 
B)  $( 3,2 )$ 
C)  $( 2,3 )$ 
D)  $( - 2,3 )$ 
E)  $( - 3 , - 2 )$

Question 11

Determine whether the ordered pair is a solution of the system of equations shown below. Ordered pair $( 2,4 )$ System of equations $x - y = - 2$ $3 x + 2 y = 14$

Accepted Answer

A) No 
B) Yes 
C) Cannot be determined

Question 12

Solve the system by any method, if possible. $$\left\{ \begin{array} { l } 
x = \frac { 3 } { 2 } y + 3 \
2 x - 3 y = 9
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 1 } { 2 } , 12 \right)$ 
B)  $\left( 12 , \frac { 3 } { 2 } \right)$ 
C)  $\left( 9 , \frac { 2 } { 3 } \right)$ 
D) infinitely many solutions, dependent equations 
E) no solution, inconsistent system

Question 13

Solve the system by elimination if possible. $$\left\{ \begin{array} { c } 
2 x + 3 y = 29 \
3 x - 2 y = - 15
\end{array} \right.$$

Accepted Answer

A) (1, 9) 
B) (1, $- 9$ ) 
C) (9, 1) 
D) infinitely many solutions, dependent equations 
E) no solution, inconsistent system

Question 14

Find the solution set of the system of inequalities. $$\left\{ \begin{array} { l } 
x + y  - 6
\end{array} \right.$$

Accepted Answer

A)   
B)   
C)

Question 15

A gift store is making a mixture of almonds, pecans, and peanuts, which sell for $3.00 per pound, $4.00 per pound, and $2.00 per pound, respectively. The storekeeper wants to make 20 pounds of the mix to sell at $2.70 per pound. The number of pounds of peanuts is to be three times the number of pounds of pecans. Find the number of pounds of each to be used in the mixture. # of almonds = __________ # of pecans = __________ # of peanuts = __________

Accepted Answer

The answer of A gift store is making a mixture...

Question 16

Use the substitution method to solve the following system: $$\left\{ \begin{array} { l } 
2 x = \frac { 1 } { 2 } y - 1.2 \
\frac { 1 } { 5 } y = 6 x - 1.6
\end{array} \right.$$

Accepted Answer

A) (-1.6, 4) 
B) (0.4, 4) 
C) (0.5, 3) 
D) The equations are dependent. 
E) The system is inconsistent.

Question 17

Tell whether the ordered pair (- 5, 3)is a solution of the given system. $$\left\{ \begin{array} { l } 
- 3 x + 8 y = 36 \
4 x - 5 y = - 31
\end{array} \right.$$

Accepted Answer

A) no 
B) yes

Question 18

Doris invested some money at 7% and some money at 8%. She invested $4,000 more at 8% than she did at 7%. Her total yearly interest from the two investments was $920. How much did Doris invest at each rate?

Accepted Answer

A) $100 at 7%, $7,900 at 8% 
B) $5,000 at 7%, $8,000 at 8% 
C) $4,000 at 7%, $9,000 at 8% 
D) $4,000 at 7%, $8,000 at 8% 
E) $4,500 at 7%, $7,500 at 8%

Question 19

Solve the system. $$\left\{ \begin{array} { c } 
x + 4 y = - 4 \
x - 4 y = - 12
\end{array} \right.$$

Accepted Answer

A)  $( 1 , - 8 )$ 
B)  $( 2,8 )$ 
C)  $( - 8,1 )$ 
D)  $( 8,1 )$ 
E)  $( 2 , - 8 )$

Question 20

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $$\left\{ \begin{array} { l } 
2 ( x + 2 ) + 9 ( y - 4 ) = 1 \
2 ( x - 1 ) = - 9 ( y + 2 )
\end{array} \right.$$

Accepted Answer

A)  $( 8,4 )$ 
B)  $( 7 , - 2 )$ 
C)  $( - 3,5 )$ 
D) The equations are dependent. 
E) The system is inconsistent.

Exam 4: Solving Systems of Equations and Inequalities

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $700,000! They agree that Susan should get $50,000 more than Maria, because she gave most of the money. How much will Maria get?

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } \frac { 1 } { 2 } x - \frac { 1 } { 6 } y = - 12 \\\frac { 1 } { 2 } x + \frac { 1 } { 4 } y = 8\end{array} \right)$

In a mix of pennies and nickels, there are 22 coins with a total value of 82 cents. How many nickels are there?

The ordered pair (1, 3)is a solution of the given system. $\left\{ \begin{array} { l } 2 x + 2 y = 8 \\4 x + 3 y = 13\end{array} \right.$

Graph the solution of the system: $\left\{ \begin{array} { l } y < 5 x - 3 \\y - 5 x \geq 4\end{array} \right.$

Consider the following system: $\left\{ \begin{array} { c } 7 x + y = 54 \\y = - 7 x - 18\end{array} \right.$ Substitute $- 7 x - 18$ for y in the first equation. How many variables does the resulting equation contain?

Solve the system by graphing. $\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.$

Use two equations in two variables to solve the following problem. At a theater, the giant rectangular movie screen has a width $24$ feet less than its length. If its perimeter is $308$ feet, find the area of the screen.

Melodic Music has compact discs on sale for either $15 or $20. If a customer wants to spend at least $60 but no more than $120 on CDs, graph a system of inequalities that will show the possible ways a customer can buy $15 CDs ( x ) and $20 CDs ( y ) .

Use the addition method to solve the system. $\left\{ \begin{array} { c } a + b = 5 \\a - b = - 1\end{array} \right.$

Determine whether the ordered pair is a solution of the system of equations shown below. Ordered pair $( 2,4 )$ System of equations $x - y = - 2$ $3 x + 2 y = 14$

Solve the system by any method, if possible. $\left\{ \begin{array} { l } x = \frac { 3 } { 2 } y + 3 \\2 x - 3 y = 9\end{array} \right.$

Solve the system by elimination if possible. $\left\{ \begin{array} { c } 2 x + 3 y = 29 \\3 x - 2 y = - 15\end{array} \right.$

Find the solution set of the system of inequalities. $\left\{ \begin{array} { l } x + y < - 6 \\x - y > - 6\end{array} \right.$

Use the substitution method to solve the following system: $\left\{ \begin{array} { l } 2 x = \frac { 1 } { 2 } y - 1.2 \\\frac { 1 } { 5 } y = 6 x - 1.6\end{array} \right.$

Tell whether the ordered pair (- 5, 3) is a solution of the given system. $\left\{ \begin{array} { l } - 3 x + 8 y = 36 \\4 x - 5 y = - 31\end{array} \right.$

Doris invested some money at 7% and some money at 8%. She invested $4,000 more at 8% than she did at 7%. Her total yearly interest from the two investments was $920. How much did Doris invest at each rate?

Solve the system. $\left\{ \begin{array} { c } x + 4 y = - 4 \\x - 4 y = - 12\end{array} \right.$ $Solve the system. \left\{ \begin{array} { c } x + 4 y = - 4 \\ x - 4 y = - 12 \end{array} \right. A) ( 1 , - 8 ) B) ( 2,8 ) C) ( - 8,1 ) D) ( 8,1 ) E) ( 2 , - 8 )$

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 ( x + 2 ) + 9 ( y - 4 ) = 1 \\2 ( x - 1 ) = - 9 ( y + 2 ) \end{array} \right.$

Exam 4: Solving Systems of Equations and Inequalities

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $700,000! They agree that Susan should get $50,000 more than Maria, because she gave most of the money. How much will Maria get?

In a mix of pennies and nickels, there are 22 coins with a total value of 82 cents. How many nickels are there?

The ordered pair (1, 3)is a solution of the given system. {2x+2y=84x+3y=13\left\{ \begin{array} { l } 2 x + 2 y = 8 \\4 x + 3 y = 13\end{array} \right.{2x+2y=84x+3y=13​

Graph the solution of the system: {y<5x−3y−5x≥4\left\{ \begin{array} { l } y < 5 x - 3 \\y - 5 x \geq 4\end{array} \right.{y<5x−3y−5x≥4​

Consider the following system: {7x+y=54y=−7x−18\left\{ \begin{array} { c } 7 x + y = 54 \\y = - 7 x - 18\end{array} \right.{7x+y=54y=−7x−18​ Substitute −7x−18- 7 x - 18−7x−18 for y in the first equation. How many variables does the resulting equation contain?

Solve the system by graphing. {4x=4−3y4x+3y=7\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.{4x=4−3y4x+3y=7​

Use two equations in two variables to solve the following problem. At a theater, the giant rectangular movie screen has a width 242424 feet less than its length. If its perimeter is 308308308 feet, find the area of the screen.

Melodic Music has compact discs on sale for either $15 or $20. If a customer wants to spend at least $60 but no more than $120 on CDs, graph a system of inequalities that will show the possible ways a customer can buy $15 CDs ( x ) and $20 CDs ( y ) .

Use the addition method to solve the system. {a+b=5a−b=−1\left\{ \begin{array} { c } a + b = 5 \\a - b = - 1\end{array} \right.{a+b=5a−b=−1​

Determine whether the ordered pair is a solution of the system of equations shown below. Ordered pair (2,4) ( 2,4 ) (2,4) System of equations x−y=−2x - y = - 2x−y=−2 3x+2y=143 x + 2 y = 143x+2y=14

Solve the system by any method, if possible. {x=32y+32x−3y=9\left\{ \begin{array} { l } x = \frac { 3 } { 2 } y + 3 \\2 x - 3 y = 9\end{array} \right.{x=23​y+32x−3y=9​

Solve the system by elimination if possible. {2x+3y=293x−2y=−15\left\{ \begin{array} { c } 2 x + 3 y = 29 \\3 x - 2 y = - 15\end{array} \right.{2x+3y=293x−2y=−15​

Find the solution set of the system of inequalities. {x+y<−6x−y>−6\left\{ \begin{array} { l } x + y < - 6 \\x - y > - 6\end{array} \right.{x+y<−6x−y>−6​

Use the substitution method to solve the following system: {2x=12y−1.215y=6x−1.6\left\{ \begin{array} { l } 2 x = \frac { 1 } { 2 } y - 1.2 \\\frac { 1 } { 5 } y = 6 x - 1.6\end{array} \right.{2x=21​y−1.251​y=6x−1.6​

Tell whether the ordered pair (- 5, 3) is a solution of the given system. {−3x+8y=364x−5y=−31\left\{ \begin{array} { l } - 3 x + 8 y = 36 \\4 x - 5 y = - 31\end{array} \right.{−3x+8y=364x−5y=−31​

Doris invested some money at 7% and some money at 8%. She invested $4,000 more at 8% than she did at 7%. Her total yearly interest from the two investments was $920. How much did Doris invest at each rate?

Solve the system. {x+4y=−4x−4y=−12\left\{ \begin{array} { c } x + 4 y = - 4 \\x - 4 y = - 12\end{array} \right.{x+4y=−4x−4y=−12​

The ordered pair (1, 3)is a solution of the given system. $\left\{ \begin{array} { l } 2 x + 2 y = 8 \\4 x + 3 y = 13\end{array} \right.$

Graph the solution of the system: $\left\{ \begin{array} { l } y < 5 x - 3 \\y - 5 x \geq 4\end{array} \right.$

Consider the following system: $\left\{ \begin{array} { c } 7 x + y = 54 \\y = - 7 x - 18\end{array} \right.$ Substitute $- 7 x - 18$ for y in the first equation. How many variables does the resulting equation contain?

Solve the system by graphing. $\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.$

Use two equations in two variables to solve the following problem. At a theater, the giant rectangular movie screen has a width $24$ feet less than its length. If its perimeter is $308$ feet, find the area of the screen.

Use the addition method to solve the system. $\left\{ \begin{array} { c } a + b = 5 \\a - b = - 1\end{array} \right.$

Determine whether the ordered pair is a solution of the system of equations shown below. Ordered pair $( 2,4 )$ System of equations $x - y = - 2$ $3 x + 2 y = 14$

Solve the system by any method, if possible. $\left\{ \begin{array} { l } x = \frac { 3 } { 2 } y + 3 \\2 x - 3 y = 9\end{array} \right.$

Solve the system by elimination if possible. $\left\{ \begin{array} { c } 2 x + 3 y = 29 \\3 x - 2 y = - 15\end{array} \right.$

Find the solution set of the system of inequalities. $\left\{ \begin{array} { l } x + y < - 6 \\x - y > - 6\end{array} \right.$

Use the substitution method to solve the following system: $\left\{ \begin{array} { l } 2 x = \frac { 1 } { 2 } y - 1.2 \\\frac { 1 } { 5 } y = 6 x - 1.6\end{array} \right.$

Tell whether the ordered pair (- 5, 3) is a solution of the given system. $\left\{ \begin{array} { l } - 3 x + 8 y = 36 \\4 x - 5 y = - 31\end{array} \right.$

Solve the system. $\left\{ \begin{array} { c } x + 4 y = - 4 \\x - 4 y = - 12\end{array} \right.$ $Solve the system. \left\{ \begin{array} { c } x + 4 y = - 4 \\ x - 4 y = - 12 \end{array} \right. A) ( 1 , - 8 ) B) ( 2,8 ) C) ( - 8,1 ) D) ( 8,1 ) E) ( 2 , - 8 )$