AnswersVT-SAT-MathModeling with Linear Systems

Solving One-Variable Equations with Systems Answers

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Carlos graphs the equations y = 0.5x2 + 3 and y = –4x2 + 24x – 35 and generates the graph below. Which conclusion is supported by the graph?

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A
The equation 0.5x2 + 3 = –4x2 + 24x – 35 has no real solutions.
B
The equation 0.5x2 + 3 = –4x2 + 24x – 35 has one real solution.
C
The equation 0.5x2 + 3 = –4x2 + 24x – 35 has two real solutions.
D
The equation 0.5x2 + 3 = –4x2 + 24x – 35 has three real solutions.
2
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Vivek graphs the equations and to solve the equation . His graph is shown below. What are the solutions of ?

Question illustration
A
–4 and 2
B
–4 and 1
C
0 and 4
D
1 and 4
3

Which system of equations can be graphed to find the solution(s) to ?

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Option A
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Option B
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Option C
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Option D
4

Heather is solving an equation by graphing the expressions on either side of the equal signs. If the graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?

A
One side of the equation is a constant, and the other side of the equation is a linear expression.
B
One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
C
One side of the equation is a constant, and the other side of the equation is a quadratic expression.
D
One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.
5

Fran graphs the equations and . Her graph is shown below. Which value is a solution of ?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

What are the two solutions of x2 – 2x – 4 = –3x + 9?

A
the y-coordinates of the y-intercepts of the graphs of y = x2 – 2x – 4 and y = –3x + 9
B
the x-coordinates of the x-intercepts of the graphs of y = x2 – 2x – 4 and y = –3x + 9
C
the y-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9
D
the x-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9
7

Which graph can be used to find the solution(s) to x2 – 1 = 3?

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Option A
B
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Option B
C
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Option C
D
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Option D
8

Michael graphs the equations and y = x + 1 to solve the equation . His graph is shown below. What are the solution(s) of ?

Question illustration
A
–1 and 8
B
1 and 4
C
2
D
3
9

Which system of equations can be graphed to find the solution(s) to x2 = 2x + 3?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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