AnswersCMS 2026-2027 NC Math 1 CREDIT RECOVERYSolving Linear-Quadratic Systems

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1
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Which represents the solution(s) of the system of equations, y plus 4 is equal to x squared and y minus x is equal to 2 ? Determine the solution set by graphing.

A
negative 2 comma 0
B
negative 2 comma 0 and 2 comma 0
C
negative 2 comma 0 and 3 comma 5
D
no solutions
2
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The first two steps in determining the solution set of the system of equations, y is equal to x squared minus 6 x plus 12 and y is equal to 2 x minus 4 , algebraically are shown in the table. Step Equation Step 1 x squared minus 6 x plus 12 is equal to 2 x minus 4 Step 2 x squared minus 8 x plus 16 is equal to 0 Which represents the solution(s) of this system of equations?

A
4 comma 4 and negative 4 comma 12
B
4 comma 4
C
negative 4 comma 4 and 4 comma 12
D
negative 4 comma negative 12
3

The first step in determining the solution to the system of equations, y is equal to negative x squared minus 4 x minus 3 and y is equal to 2 x plus 5 , algebraically is to set the two equations equal as negative x squared minus 4 x minus 3 is equal to 2 x plus 5 What is the next step?

A
Combine like terms onto one side of the equation.
B
Factor each side of the equation.
C
Use substitution to create a one-variable equation.
D
Set y is equal to 0 in y is equal to negative x squared minus 4 x minus 3 .
4

Which represents the solution(s) of the graphed system of equations, y is equal to x squared plus x minus 2 and y is equal to 2 x minus 2 ? Open image in full-screen view

A
negative 2 comma 0 and 0 comma 1
B
negative 2 comma 0 and 1 comma 0
C
0 comma negative 2 and 0 comma 1
D
0 comma negative 2 and 1 comma 0
5

Which represents the solution(s) of the graphed system of equations, y is equal to x squared plus 2 x minus 3 and y is equal to x minus 1 ? Open image in full-screen view

A
negative 3 comma negative 2 and 0 comma 1
B
negative 2 comma negative 3 and 1 comma 0
C
0 comma negative 3 and 1 comma 0
D
1 comma 0 and 0 comma negative 1
6

Which graph shows a system of equations with a solution at negative 1 comma 1 ?

A
Image with description A coordinate plane with x-axis and y-axis labeled from negative 5 to 5 in increments of 1. Two functions are plotted on the grid, a quadratic function and a linear function. The parabola opens upwards with its vertex at 0 comma negative 2. It passes through the x-axis at negative 1 comma 0 and 1 comma 0, and extends upwards into the first and second quadrants with arrowheads pointing near negative 2 comma 5 and 2 comma 5. The line has a positive slope, passing through the y-axis at 0 comma negative 1 and the x-axis at 1 comma 0.
B
Image with description A coordinate plane with x-axis and y-axis labeled from negative 5 to 5 in increments of 1. Two functions are plotted on the grid, a quadratic function and a linear function. The parabola opens downwards with its vertex at 0 comma 3. It passes through the x-axis near negative 1 point 7 comma 0 and 1 point 7 comma 0, and extends downwards into the third and fourth quadrants with arrowheads pointing near negative 2 comma negative 5 and 2 comma negative 5. The line has a positive slope, passing through the y-axis at 0 comma 2 and the x-axis at negative 2 comma 0.
C
Image with description A coordinate plane with x-axis and y-axis labeled from negative 5 to 5 in increments of 1. Two functions are plotted on the grid, a quadratic function and a linear function. The parabola opens upwards with its vertex at 0 comma negative 2. It passes through the x-axis at negative 1 comma 0 and 1 comma 0, and extends upwards into the first and second quadrants with arrowheads pointing near negative 2 comma 5 and 2 comma 5. The line has a negative slope, passing through the y-axis at 0 comma negative 1 and the x-axis at negative 1 comma 0.
D
Image with description A coordinate plane with x-axis and y-axis labeled from negative 5 to 5 in increments of 1. Two functions are plotted on the grid, a quadratic function and a linear function. The parabola opens downwards with its vertex at 0 comma 1. It passes through the x-axis near negative 1 comma 0 and 1 comma 0, and extends downwards with arrowheads pointing near negative 1 point 7 comma negative 5 and 1 point 7 comma negative 5. The line has a positive slope, passing through the y-axis at 0 comma negative 2 and the x-axis at 2 comma 0.
7

Which represents the solution(s) of the system of equations, y is equal to negative x squared plus 6 x plus 16 and y is equal to negative 4 x plus 37 ? Determine the solution set algebraically.

A
3 comma 25 and 7 comma 9
B
3 comma 25
C
negative 3 comma 49 and negative 7 comma 65
D
negative 3 comma 49
8

The first two steps in determining the solution set of the system of equations, y is equal to x squared minus 2 x minus 3 and y is equal to negative x plus 3 , algebraically are shown in the table. Step Equation Step 1 x squared minus 2 x minus 3 is equal to negative x plus 3 Step 2 0 is equal to x squared minus x minus 6 Which represents the solution(s) of this system of equations?

A
negative 6 comma 9 and 1 comma 2
B
6 comma negative 3 and negative 1 comma 4
C
negative 3 comma 6 and 2 comma 1
D
3 comma 0 and negative 2 comma 5
9

Which graph most likely shows a system of equations with no solutions?

A
Image with description A coordinate plane with a parabola and a straight line. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex near 0 comma 0 at the origin, with the left arm rising into the upper-left portion of the plane and the right arm rising into the upper-right area. The straight line has a negative slope and extends from the upper-left area of the plane, passing through approximately negative 1 comma 4, downward to the right, ending near the point 2 comma negative 5.
B
Image with description A coordinate plane with a parabola and a straight line. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex near 0 comma 2, with both arms rising steeply into the upper portion of the plane. The straight line has a positive slope and extends from the lower-left area of the plane, passing through approximately negative 3 comma negative 4, upward to the right, passing through approximately 3 comma 4.
C
Image with description A coordinate plane with a parabola and a straight line. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex near 0 comma 1 on the y-axis, with both arms rising into the upper portion of the plane. The straight line has a slight positive slope and extends from the lower-left area of the plane, passing through approximately negative 5 comma negative 4, to the right edge of the plane near 5 comma 0.
D
Image with description A coordinate plane with a parabola and a straight line. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex near 0 comma 1 on the y-axis, with both arms rising steeply into the upper portion of the plane. The straight line has a slight positive slope and extends from the lower-left area of the plane, passing through approximately negative 4 comma negative 4, to the right edge near 5 comma 1.
10

Which graph most likely shows a system of equations with one solution?

A
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. An upward-opening parabola and a straight line are plotted. The parabola has a y-intercept at the point 0 comma 1. The straight line has a positive slope and passes through the point 3 comma 0 and the point 0 comma negative 3.
B
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A downward-opening parabola has a vertex at approximately the point 0 comma 1. It passes through approximately the points negative 1 comma 0 and 1 comma 0, then continues downward beyond the bottom of the graph on both sides. A straight line with a positive slope passes through approximately the points 0 comma negative 3, 2 comma negative 2, and 4 comma negative 1. The parabola and the line intersect at approximately the points negative 1.5 comma negative 3.8 and 1.1 comma negative 2.4.
C
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A downward-opening parabola and a straight line are plotted. The parabola has a vertex at the point 0 comma 1. The straight line has a positive slope and passes through the point 0 comma negative 3 and the point 2 comma negative 2.
D
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A downward-opening parabola and a straight line are plotted. The parabola has a vertex at the point 0 comma 1. The straight line has a positive slope and passes through the point 0 comma 3 and the point negative 3 comma negative 3.

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