AnswersCMS 2026-2027 NC Math 1 CREDIT RECOVERYSolving Systems of Linear Equations: Graphing

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A system of equations has an infinite number of solutions. 3⁢y−4⁢x=5 3⁢y+b⁢x=c What are the values of b and c ? Enter your answer in the boxes.

Answer:

-4|5

2
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A student says, "The x-coordinate of the intersection point is a solution to f⁡(x)=g⁡(x) only because these two graphs happen to be straight lines." Is the student correct?

A
No, this only works when both slopes are positive.
B
No, any intersection point solves f of x is equal to g of x .
C
Yes, but only when the intersection point is above the x -axis.
D
Yes, this only works for linear functions.
3

How many solutions does this linear system have? y is equal to 2 x minus 5 negative 8 x minus 4 y is equal to negative 20

A
one solution: negative 2 point 5 comma 0
B
one solution: 2 point 5 comma 0
C
infinite number of solutions
D
no solution
4

A system of equations has no solution. If y is equal to 8 x plus 7 is one of the equations, which could be the other equation?

A
y is equal to 8 x minus 7
B
y is equal to negative 8 x plus 7
C
2 y is equal to negative 16 x minus 14
D
2 y is equal to 16 x plus 14
5

How many solutions does this linear system have? y is equal to negative 1 half x plus 4 x plus 2 y is equal to negative 8

A
one solution: 8 comma 0
B
one solution: 0 comma 8
C
no solution
D
infinite number of solutions
6

How many solutions does this linear system have? y is equal to negative 6 x plus 2 negative 12 x minus 2 y is equal to negative 4

A
one solution: 0 comma 0
B
one solution: 1 comma negative 4
C
infinite number of solutions
D
no solution
7

A system of equations has infinitely many solutions. If 2 y minus 4 x is equal to 6 is one of the equations, which could be the other equation?

A
negative y is equal to negative 2 x minus 3
B
negative y is equal to negative 4 x plus 6
C
y is equal to 4 x plus 6
D
y is equal to 2 x plus 6
8

Sylvie finds the solution to the system of equations by graphing. y is equal to 2 thirds x plus 1 and y is equal to negative 2 thirds x minus 1 Which graph shows the solution to Sylvie’s system of equations?

A
Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 0 2 comma 0 point 6 3, 0 comma negative 1, and 2 comma negative 4. The second line passes through the points negative 1 point 0 2 comma 0 point 6 3, 0 comma 1, and 3 comma 2.
B
Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 7 comma 1 point 5 7, 0 comma 1, and 3 comma 0. The second line passes through the points negative 1 point 7 comma 1 point 5 7, 0 comma negative 1, and 2 comma negative 4.
C
Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 5 comma 0, 0 comma negative 1, and 3 comma negative 3. The second line passes through the points negative 1 point 5 comma 0, 0 comma 1, and 3 comma 3.
D
Image with description A coordinate grid with 2 lines. The x and y-axes are labeled from negative 5 to 5 in increments of 1. The first line passes through the points negative 1 point 7 1 comma 0 point 1 4, 0 comma negative 1, and 3 comma negative 3. The second line passes through the points negative 1 point 7 1 comma 0 point 1 4, 0 comma 1, and 2 comma 2.
9

A system of equations has 1 solution. If 4 x minus y is equal to 5 is one of the equations, which could be the other equation?

A
y is equal to negative 4 x plus 5
B
2 y is equal to 8 x minus 10
C
negative 2 y is equal to negative 8 x minus 10
D
y is equal to 4 x minus 5
10

How many solutions does this linear system have? y is equal to negative 6 x plus 2 negative 12 x minus 2 y is equal to negative 4

A
one solution: 0 comma 0
B
one solution: 1 comma negative 4
C
infinite number of solutions
D
no solution

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