Question 1

The perimeter of a rectangle is 78 inches. The width of the rectangle is 9 inches less than the length of the rectangle. Find the dimensions of the rectangle.

Accepted Answer

A) The dimensions of the rectangle are 15 inches by 24 inches. 
B) The dimensions of the rectangle are 14 inches by 23 inches. 
C) The dimensions of the rectangle are 13 inches by 22 inches. 
D) The dimensions of the rectangle are 16 inches by 25 inches. 
E) The dimensions of the rectangle are 17 inches by 26 inches. 
A) The dimensions of the rectangle are 15 inches by 24 inches. 
B) The dimensions of the rectangle are 14 inches by 23 inches. 
C) The dimensions of the rectangle are 13 inches by 22 inches. 
D) The dimensions of the rectangle are 16 inches by 25 inches. 
E) The dimensions of the rectangle are 17 inches by 26 inches.

Question 2

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $400,000! 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) $230,000 
B) $225,000 
C) $75,000 
D) $175,000 
E) $90,000 
A) $230,000 
B) $225,000 
C) $75,000 
D) $175,000 
E) $90,000

Question 3

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

Question 4

Solve the system of equations by graphing. $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } = 98 \
x + y = 14
\end{array} \right.$$

Accepted Answer

A)  $( - 49,8 )$ 
B)  $( 49 , - 49 )$ 
C)  $( 8,5 )$ 
D)  $( 5,8 )$ 
E)  $( 7,7 )$ 
A)  $( - 49,8 )$ 
B)  $( 49 , - 49 )$ 
C)  $( 8,5 )$ 
D)  $( 5,8 )$ 
E)  $( 7,7 )$

Question 5

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $$\left\{ \begin{array} { c } 
y = 4 x \
x + y = 5
\end{array} \right.$$

Accepted Answer

A)  $( 1,4 )$ 
B)  $( 5,2 )$ 
C)  $( 4,1 )$ 
D) The equations are dependent. 
E) The system is inconsistent. 
A)  $( 1,4 )$ 
B)  $( 5,2 )$ 
C)  $( 4,1 )$ 
D) The equations are dependent. 
E) The system is inconsistent.

Question 6

Part of $9,000 is invested at 11%, another part at 13%, and the remainder at 15% yearly interest. The total yearly income from the three investments is $1,210. The sum of the amounts invested at 11% and 13% equals the amount invested at 15%. Determine how much is invested at each rate, if 2,500 is invested at first rate.

Accepted Answer

A) $2,500 at 11%, $2,000 at 13%, and $4,500 at 15% 
B) $3,000 at 11%, $1,000 at 13%, and $4,000 at 15% 
C) $3,500 at 11%, $1,000 at 13%, and $4,500 at 15% 
D) $3,000 at 11%, $2,000 at 13%, and $4,000 at 15% 
E) $2,000 at 11%, $3,000 at 13%, and $3,500 at 15% 
A) $2,500 at 11%, $2,000 at 13%, and $4,500 at 15% 
B) $3,000 at 11%, $1,000 at 13%, and $4,000 at 15% 
C) $3,500 at 11%, $1,000 at 13%, and $4,500 at 15% 
D) $3,000 at 11%, $2,000 at 13%, and $4,000 at 15% 
E) $2,000 at 11%, $3,000 at 13%, and $3,500 at 15%

Question 7

Use two equations in two variables to find the following integers. The sum of two integers is 34 and their difference is 8.

Accepted Answer

A) 8, 26 
B) 11, 19 
C) 13, 19 
D) 13, 21 
E) 11, 26 
A) 8, 26 
B) 11, 19 
C) 13, 19 
D) 13, 21 
E) 11, 26

Question 8

Determine the graph of the system of equations. $$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 2 \
- x + y = 2
\end{array} \right.$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Determine the graph of the system of equations. $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } = 25 \
x - y = - 1
\end{array} \right.$$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Use two equations in two variables to find the following integers: One integer is twice another. Their sum is 39.

Accepted Answer

A) 13, 26 
B) 26, 52 
C) 13, 52 
D) 16, 23 
E) no such integers exist 
A) 13, 26 
B) 26, 52 
C) 13, 52 
D) 16, 23 
E) no such integers exist

Question 11

Find the number of points of intersection of the system $$\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } = 49 \
x - y = 36
\end{array} \right.$$

Accepted Answer

A) four 
B) two 
C) zero 
D) one 
A) four 
B) two 
C) zero 
D) one

Question 12

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $$\left\{ \begin{array} { c } 
7 a + 7 b = 42 \
a = 46 - 9 b
\end{array} \right.$$

Accepted Answer

A)  $( 1,5 )$ 
B)  $( 1 , - 5 )$ 
C)  $( - 1,5 )$ 
D) The equations are dependent. 
E) The system is inconsistent. 
A)  $( 1,5 )$ 
B)  $( 1 , - 5 )$ 
C)  $( - 1,5 )$ 
D) The equations are dependent. 
E) The system is inconsistent.

Question 13

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $$\left\{ \begin{array} { l } 
6 ( x + 6 ) + 5 ( y - 4 ) = 6 \
6 ( x - 1 ) = - 5 ( y + 2 )
\end{array} \right.$$

Accepted Answer

A)  $( 4,5 )$ 
B)  $( 1 , - 7 )$ 
C)  $( - 4,1 )$ 
D) The equations are dependent. 
E) The system is inconsistent. 
A)  $( 4,5 )$ 
B)  $( 1 , - 7 )$ 
C)  $( - 4,1 )$ 
D) The equations are dependent. 
E) The system is inconsistent.

The perimeter of a rectangle is 78 inches. The width of the rectangle is 9 inches less than the length of the rectangle. Find the dimensions of the rectangle.

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $400,000! 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. $\left\{ \begin{array} { c } x + 4 y = - 4 \\x - 4 y = - 12\end{array} \right.$ $Solve the system. \left\{ \begin{array} { c } x + 4 y = - 4 \\ x - 4 y = - 12 \end{array} \right.$

Solve the system of equations by graphing. $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 98 \\x + y = 14\end{array} \right.$ $Solve the system of equations by graphing. \left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 98 \\ x + y = 14 \end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } y = 4 x \\x + y = 5\end{array} \right.$

Use two equations in two variables to find the following integers. The sum of two integers is 34 and their difference is 8.

Determine the graph of the system of equations. $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 2 \\- x + y = 2\end{array} \right.$

Determine the graph of the system of equations. $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 25 \\x - y = - 1\end{array} \right.$

Use two equations in two variables to find the following integers: One integer is twice another. Their sum is 39.

Find the number of points of intersection of the system $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 49 \\x - y = 36\end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } 7 a + 7 b = 42 \\a = 46 - 9 b\end{array} \right.$

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $\left\{ \begin{array} { l } 6 ( x + 6 ) + 5 ( y - 4 ) = 6 \\6 ( x - 1 ) = - 5 ( y + 2 )\end{array} \right.$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Exponential and Logarithmic Functions

Filters

Exam 10: Systems of Equations

The perimeter of a rectangle is 78 inches. The width of the rectangle is 9 inches less than the length of the rectangle. Find the dimensions of the rectangle.

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $400,000! 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. {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​

Solve the system of equations by graphing. {x2+y2=98x+y=14\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 98 \\x + y = 14\end{array} \right.{x2+y2=98x+y=14​

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. {y=4xx+y=5\left\{ \begin{array} { c } y = 4 x \\x + y = 5\end{array} \right.{y=4xx+y=5​

Use two equations in two variables to find the following integers. The sum of two integers is 34 and their difference is 8.

Determine the graph of the system of equations. {x2+y2=2−x+y=2\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 2 \\- x + y = 2\end{array} \right.{x2+y2=2−x+y=2​

Determine the graph of the system of equations. {x2+y2=25x−y=−1\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 25 \\x - y = - 1\end{array} \right.{x2+y2=25x−y=−1​

Use two equations in two variables to find the following integers: One integer is twice another. Their sum is 39.

Find the number of points of intersection of the system {x2+y2=49x−y=36\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 49 \\x - y = 36\end{array} \right.{x2+y2=49x−y=36​

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. {7a+7b=42a=46−9b\left\{ \begin{array} { c } 7 a + 7 b = 42 \\a = 46 - 9 b\end{array} \right.{7a+7b=42a=46−9b​

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Exponential and Logarithmic Functions

Filters

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

Solve the system of equations by graphing. $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 98 \\x + y = 14\end{array} \right.$ $Solve the system of equations by graphing. \left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 98 \\ x + y = 14 \end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } y = 4 x \\x + y = 5\end{array} \right.$

Determine the graph of the system of equations. $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 2 \\- x + y = 2\end{array} \right.$

Determine the graph of the system of equations. $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 25 \\x - y = - 1\end{array} \right.$

Find the number of points of intersection of the system $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 49 \\x - y = 36\end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } 7 a + 7 b = 42 \\a = 46 - 9 b\end{array} \right.$