AnswersGA-GSE Algebra IIAdvanced Algebra BSolving One-Variable Equations with Systems

Solving One-Variable Equations with Systems Answers

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
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Option
Option D
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Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below.What are the solutions of –x2 + 4x = x – 4?

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

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
4

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Question illustration
A
–1 and 3
B
0 and 2
C
1
D
3
6

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?

Question illustration
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.
7

What are the two solutions of 2x2 = –x2 – 5x – 1?

A
the y-coordinates of the intersection points of the graphs of y = 2x2 and y = –x2 – 5x – 1
B
the x-coordinates of the x-intercepts of the graphs of y = 2x2 and y = –x2 – 5x – 1
C
the x-coordinates of the intersection points of the graphs of y = 2x2 and y = –x2 – 5x – 1
D
the y-coordinates of the y-intercepts of the graphs of y = 2x2 and y = –x2 – 5x – 1
8

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
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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