AnswersAdv. Algebra II S1 OriginalSolving Linear Systems Graphically

Solving Linear Systems Graphically Answers

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

5

3

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Answer:

-2

4

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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

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 +

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Blank 1:-2
Blank 2:5
Blank 3:-2
Blank 4:3
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 +

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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

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?

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Blank 1:-2
Blank 2:3
Blank 3:3
Blank 4:-7
14

✔ 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
15

Which statements did you include in your answer?

A
The slopes are different.
B
The y-intercepts are different.
16

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.

17

How should you modify the graph to show the solution to the system of inequalities below? Check all that apply.

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.
18

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

A
✔ no solution.
B
exactly one solution.
C
infinitely many solutions.
19

Question text not available

Answer:

-3

20

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

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

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