AnswersAG Q4 Keystone Algebra 1 Block 25-26 DDiamondUsing Graphs to Determine the Number of Solutions

Using Graphs to Determine the Number of Solutions Answers

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1
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Given the graph of a system of equations, which statements are true about the solution? Check all that apply.

A
The x-value is an integer.
B
The x-value is between 3 and 4.
C
The y-value is between –2 and –1.
D
The x-value is positive.
E
The x- and y-values have the same sign.
2
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Which integers is the x-coordinate between?✔ 0 and 11 and 22 and 33 and 4

A
✔ 0 and 1
B
1 and 2
C
2 and 3
D
3 and 4
3

Which integers is the y-coordinate between?0 and 11 and 2✔ 2 and 33 and 4

A
0 and 1
B
1 and 2
C
✔ 2 and 3
D
3 and 4
4

What is the solution approximated to the tenths place?(1.1, 2.9)✔ (0.4, 2.8)(1.8, 2.1)(2.9, 1.3)

A
(1.1, 2.9)
B
✔ (0.4, 2.8)
C
(1.8, 2.1)
D
(2.9, 1.3)
5

For which system of equations would you need to estimate the solution?

A
On a coordinate plane, 2 lines intersect at (3, 0).
Option A
B
On a coordinate plane, 2 lines intersect around (negative 2.1, negative 3.5).
Option B
C
On a coordinate plane, 2 lines intersect at (negative 2, 3).
Option C
D
On a coordinate plane, 2 lines intersect at (2, 2).
Option D
6

What is the approximate value for the y-coordinate?

A
y –1.1
Option A
B
y –1.4
Option B
C
y –1.8
Option C
D
y –1.9
Option D
7

How can the solution be located? Which integers is the x-coordinate between? Which integers is the y-coordinate between? What is the solution approximated to the tenths place?

Answers:
Selection 1:find the intersection
Selection 2:0 and 1
Selection 3:2 and 3
Selection 4:(0.4, 2.8)
8

Sadira estimated the solution of a system of equations is approximately (–3.7, 2.2). What can be concluded of the graph that represents the system of this solution? Check all that apply.

A
The x-coordinate of the intersection point is between 2 and 3.
B
The y-coordinate of the intersection point is between 2 and 3.
C
The y-coordinate of the intersection point is between –3 and –4.
D
The x-coordinate is closer to –4 than –3.
E
The y-coordinate is closer to –4 than –3.
9

Which graph shows a system of equations with an estimated solution of (–3.4, 1.2)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Analyze Tyrone’s estimated solution. Is he correct? If not, what was his mistake?

A
Yes, Tyrone is correct.
B
No, he did not use the intersection point.
C
No, the x-coordinate is closer to –3 than –2.
D
No, he switched the x- and y-coordinate values.
11

Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?

A
On a coordinate plane, 2 lines intersect at (3, 0).
Option A
B
On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
Option B
C
On a coordinate plane, 2 lines intersect at (negative 1.5, 1).
Option C
D
On a coordinate plane, 2 lines intersect at (1.5, 2.5).
Option D

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