Using Substitution to Solve Systems

Which system of equations below has no solution?

• y = 4x + 5 and y = 4x – 5

• y = 4x + 5 and 2y = 8x + 10

• y = 4x + 5 and y = 1/4x + 5

• y = 4x + 5 and y = 8x + 10

Which system of equations below has infinitely many solutions?

• y = –3x + 4 and y = –3x – 4

• y = –3x + 4 and 3y = –9x + 12

• y = –3x + 4 and y = -1/3x + 4

• y = –3x + 4 and y = –6x + 8

Which system of equations below has exactly one solution?

• y = –8x – 6 and y = –8x + 6

• y = –8x – 6 and 1/2y = –4x – 3

• y = –8x – 6 and y = 8x – 6

• y = –8x – 6 and –y = 8x + 6

A system of equations is given:

 $y=\frac{1}{2}x-3\ \ and\ \ y=\ -\frac{1}{2}x-3$  

Which of the following statements best describes the two lines?

• They have the same slope but different y-intercepts, so they have no solution.

• They have the same slope but different y-intercepts, so they have one solution.

• They have different slopes but the same y-intercept, so they have no solution.

• They have different slopes but the same y-intercept, so they have one solution.

 $y=-2x+\frac{1}{4}\ \ and\ \ y=-2x-\frac{1}{4}$  

A system of equations is given :

Which of the following statements best describes the two lines?

• They have the same slope but different y-intercepts, so they have no solution.

• They have the same slope but different y-intercepts, so they have one solution.

• They have different slopes but the same y-intercept, so they have no solution.

• They have different slopes but the same y-intercept, so they have one solution.

 $y=-\frac{1}{3}x+6\ \ and\ \ x=-6$  

What is the solution to the system of equations?

• (–6, 8)

• (–6, 4)

• (8, –6)

• (4, –6)

 $y=\frac{2}{5}x-3\ \ and\ x=-10$  

What is the solution to the system of equations ?

• (–10, –7)

• (–10, –1)

• (–7, –10)

• (–1, –10)

 $y=-\frac{3}{4}x+3\ \ and\ y=-12$  

What is the solution to the system of equations?

• (20, –12)

• (12, –12)

• (–6, –12)

• (–12, 12)

 $y=-\frac{1}{3}x+6\ \ and\ \ y=\frac{1}{3}x-6$  

What is the solution to the system of equations?

• no solution

• infinitely many solutions

• (–18, 12)

• (18, 0)

 $y=-2x-6\ \ and\ \ 2y=-4x-12$  

What is the solution to the system of equations?

• no solution

• infinitely many solutions

• (–3, 0)

• (3, –12)