Question

A system of linear equations for the variables x and y is shown.
y=-x-4
3y=cx-18
For what value of c, if any, will this system have no solution? Justify your answer.

Answer 1

Answer: -3

Step-by-step explanation:

Given

Equations of the lines are

$y=-x-4\\3y=cx-18$

For the system of linear equation $a_1x+b_1y=c_1,a_2x+b_2y=c_2$ has no solution if

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$

Rewrite the equations

$x+y=-4,\ cx-3y=18$

Insert the values for the no solution condition

$\Rightarrow \dfrac{1}{c}=\dfrac{1}{-3}\\\\\Rightarrow c=-3$

Therefore, for c=-3, the system of linear equation ha no solution.