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

Solving One-Variable Equations with Systems Answers

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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
2
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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
3

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
4

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

Question illustration
A
mc010-5.jpg
Option A
B
mc010-6.jpg
Option B
C
mc010-7.jpg
Option C
D
mc010-8.jpg
Option D
5

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.
6

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
7

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
8

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
9

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
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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