Systems of Linear Equations Unit Test
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)
left parenthesis 2 comma 7 right parenthesis
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)
(
)
(2, 4)
This is the estimated solution to the system of linear equations based on the graph provided.
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
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.
Question
Solve the system of equations.
4x−8y=−36
−6x+y=32 (1 point)
(
,
)
(4, 4)
Solving the system of equations by either substitution or elimination method will lead to the solution (4, 4).
Systems of Linear Equations Unit Test
8 of 148 of 14 Items
Question
Solve the system of equations.
6x−3y=−6
9x−3y=−18 (1 point)
(
,
)
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.
Solve the system of equations.
6x−3y=−6
9x−3y=−18