AnswersFL-1200330-Algebra 2 CRUnit Test

Solving Linear Systems Graphically Answers

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Analyze the solution set of the following system by following the given steps. 2x + y = 5 3y = 9 − 6x Write each equation in slope-intercept form. y = x + y = x +

Answers:
Blank 1:-2
Blank 2:5
Blank 3:-2
Blank 4:3
2
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Question text not available

Answer:

5

3

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Answer:

-2

4

Question text not available

Answer:

3

5

What do the equations have in common? How are they different?

Answer:

The equations have the same slope, -2, but different y-intercepts, 5 and 3.

6

Question text not available

Answers:
The system represents lines that , therefore the system has .:intersect at one point
The system represents lines that , therefore the system has .:exactly one solution
7

intersect at one pointcoincide✔ are parallel

Answers:
The system represents lines that , therefore the system has .:are parallel
The system represents lines that , therefore the system has .:no solution.
8

Which statements did you include in your answer?

A
The slopes are the same.
B
The y-intercepts are different.
9

Solve the system. 2x + y = −3 −2y = 6 + 4x Write each equation in slope-intercept form. y = x + y = x +

Answers:
Blank 1:-2
Blank 2:-3
Blank 3:-2
Blank 4:-3
10

intersect at one point✔ coincideare parallel

Answers:
The system represents lines that , therefore the system has .:coincide
The system represents lines that , therefore the system has .:infinitely many solutions.
11

Which statements did you include in your answer?

A
The slopes are the same.
B
The y-intercepts are the same.
C
The lines are the same.
12

Consider the system:y = 3x + 5y = ax + bWhat values for a and b make the system inconsistent? What values for a and b make the system consistent and dependent? Explain.

Answer:

The system is inconsistent when a = 3 and b ≠ 5. It is consistent and dependent when a = 3 and b = 5.

13

Which statements did you include in your answer?

A
Option
Option A
B
Option
Option B
C
Option
Option C
14

Solve the system. 2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form. y = x + y = x + How do the slopes and y–intercepts of the two equations compare?

Answers:
Blank 1:-2
Blank 2:3
Blank 3:3
Blank 4:-7
15

✔ intersect at one pointcoincideare parallel

Answers:
The system represents lines that , therefore the system has .:intersect at one point
The system represents lines that , therefore the system has .:exactly one solution
16

Which statements did you include in your answer?

A
The slopes are different.
B
The y-intercepts are different.
17

Explain how you can determine that the following system has one unique solution – without actually solving the system.

Question illustration
Answer:

Rewrite both equations in slope-intercept form. Their slopes are −2 and −1, so the lines intersect at exactly one point. That intersection is the system’s unique solution.

18

Which statements did you include in your answer?

A
Write each equation in slope-intercept form.
B
Find that the slope of the first line is –2.
C
Find that the slope of the second line is –1.
D
Since the slopes of the lines are different, the lines must have a point of intersection.
E
The point of intersection is the unique solution.
19

How should you modify the graph to show the solution to the system of inequalities below? Check all that apply. [image 1] [image 2]

Question illustration
A
Shade above 2x + y = 4.
B
Shade below 2x + y = 4.
C
Shade above 2y = 6 – 2x.
D
Shade below 2y = 6 – 2x.
E
Make the boundary line 2x + y = 4 dashed.
20

✔ no solution.exactly one solution.infinitely many solutions.

A
✔ no solution.
B
exactly one solution.
C
infinitely many solutions.

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