Which equation, when graphed with the given equation, will form a system that has no solution? y = 3x+6
y=-3(x+6)
y=-3(x-2)
y = 3(x-2)

y = -3(x + 6)  and y = -3(x - 2)

Step-by-step explanation:

A system that has no solutions means that the lines do not intersect at any point meaning the lines are parallel to each other, and for lines to be parallel to each other the slope of the lines should be equal since parallel lines have same slope.

So the equation of the line in the graph is y = -3x + 6

and the equation when graphed will form a system that has no solution is

y = -3(x + 6)  and y = -3(x - 2)

both have same slope to the slope of the line graphed in the figure that is -3

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2