5.2 Solving Systems by Substitution

Which ordered pair is a solution to the system:

 $x=2y+5$  
 $2x-3y=7$  

• (-1, 3)

• (1, -3)

• (-1, -3)

• (3, 1)

The equation of two lines are 2x - 3y = 12 and x = 4y + 1.

What is the value of x in the solution for this system of equations?

• 2

• 9

• -2

• -9

Solve the system of equations:

 $y=6x+4$  
 $y=-3x-5$  

• (-1, -2)

• (-2, -1)

• (1, -2)

• (1, 2)

Solve the system of equations:

 $x=-4y+5$  
 $x+4y=10$  

• (2, 5)

• No Solution

• Infinite Solutions

• (5, 10)

Three hundred fifty-eight tickets were sold to the school basketball game on Friday. Student tickets were $1.50 and adult tickets were $3.25. The school made $752.25. Which system could be used to find the number of student and adult tickets that were sold?

• 
• 
• 
• 

Naomi took a 40-question history exam. The exam only had multiple-choice questions and short-answer questions. Each multiple-choice question was worth one point; each short-answer question was worth five points; the whole exam was worth 100 points. Which system of equations could be used to solve for m, the number of multiple-choice questions, and s, the number of short-answer questions?

• 
• 
• 
• 

The perimeter of a rectangle is 128 inches. If the length is triple the width, set up and solve a system of equations to determine the length and width of the rectangle.

• Length =16 and Width = 48

• Length =48 and Width = 16

• Length =96 and Width = 32

• Length =32 and Width = 96

Solve the system of equations: 

 $y\ -3x=2$  
 $y=-3x+8$  

• (5,1)

• (-1, 5)

• (1, 5)

• (-5, -1)

Solve the system of equations:

 $y\ =\ \frac{1}{4}x+3$  
 $y\ =x-3$  

• (5, 3)

• (3, 8)

• (3, 5)

• (8, 5)

Solve the system of equations:
 $y=3x+13$  

 $y+22=-2x$  

• (-7,-8)

• (7, -8)

• (-7, 8)

• (7, 8)