AnswersFL-1200340-Algebra 2 HonorsSolving One-Variable Equations with 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?

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.
2
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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
3

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.
4

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
5

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
6

What is the solution of 3x + 5 = 2x – 7?

A
the x-coordinates of the intersection point of the lines y = 3x + 5 and y = 2x – 7
B
the x-coordinates of the x-intercepts of the lines y = 3x + 5 and y = 2x – 7
C
the y-coordinate of the intersection point of the lines y = 3x + 5 and y = 2x – 7
D
the y-coordinates of the y-intercepts of the lines y = 3x + 5 and y = 2x – 7
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

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
9

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
D
Option
Option D
10

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

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