Systems of Linear Equations Unit Test

Question

2 of 142 of 14 Items

Question
Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x axis extending from negative 10 to 10 in increments of 1 and the y axis extending from negative 5 to 15 in increments of 1. A solid line and a dotted line with arrows at both ends intersect each other. The equation of the solid line is y equals one half x plus 6. The equation of the dotted line is y equals 2 x plus 3. The lines intersect at left parenthesis 2 comma 7 right parenthesis which is not plotted as a point.

Estimate the solution to the system of these linear equations based on the graph.

y=2x+3
y=12x+6(1 point)
Responses

(7, 2)
left parenthesis 7 comma 2 right parenthesis

(−2, 7)
left parenthesis negative 2 comma 7 right parenthesis

(2,−7)
left parenthesis 2 comma negative 7 right parenthesis

(2, 7)

Answer 1

left parenthesis 2 comma 7 right parenthesis

Answer 2

Systems of Linear Equations Unit Test
3 of 143 of 14 Items

Question
Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals 3 x minus 2. The equation of the dotted line is y equals negative x plus 6. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.

Estimate the solution to the system of these linear equations based on the graph.

y=−x+6

y=3x−2

(1 point)
(
)

Answer 3

(2, 4)

This is the estimated solution to the system of linear equations based on the graph provided.

Answer 4

Determine the number of solutions to this system of linear equations:
2x+y=6
4x+2y=8(1 point)
Responses

infinite
infinite

2
2

1
1

0

Answer 5

1

This system of linear equations has 1 solution because the two equations are essentially the same, with one being a multiple of the other.

Answer 6

Question
Solve the system of equations.
4x−8y=−36
−6x+y=32 (1 point)
(
,
)

Answer 7

(4, 4)

Solving the system of equations by either substitution or elimination method will lead to the solution (4, 4).

Answer 8

Systems of Linear Equations Unit Test
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Question
Solve the system of equations.
6x−3y=−6
9x−3y=−18 (1 point)
(
,
)

Answer 9

This system of equations is inconsistent because the two equations represent parallel lines with the same slope but different y-intercepts. As a result, they will never intersect and have no solution.

Answer 10

Solve the system of equations.
6x−3y=−6
9x−3y=−18

Answer 11

To solve this system of equations, notice that the two equations have the same y-coefficient (-3y). This implies that the lines are parallel, which means they will never intersect and there is no solution to this system of equations.