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

Solving One-Variable Equations with Systems Answers

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1
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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
2
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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
3

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

A
mc015-1.jpg
Option A
B
mc015-2.jpg
Option B
C
mc015-3.jpg
Option C
D
mc015-4.jpg
Option D
4

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
5

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

A
mc018-1.jpg
Option A
B
mc018-2.jpg
Option B
C
mc018-3.jpg
Option C
D
mc018-4.jpg
Option D
6

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

A
mc005-1.jpg
Option A
B
mc005-2.jpg
Option B
C
mc005-3.jpg
Option C
D
mc005-4.jpg
Option D
7

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

A
mc016-1.jpg
Option A
B
mc016-2.jpg
Option B
C
mc016-3.jpg
Option C
D
mc016-4.jpg
Option D
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

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.
10

Tiffany is solving an equation where both sides are quadratic expressions. She sets each quadratic equation equal to y and graphs the resulting system. If the graph of one quadratic opens upward and the other opens downward, what is the greatest possible number of intersections for these graphs?

A
none
B
one
C
two
D
infinitely many

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