Answer: -3
Step-by-step explanation:
Given
Equations of the lines are
[tex]y=-x-4\\3y=cx-18[/tex]
For the system of linear equation [tex]a_1x+b_1y=c_1,a_2x+b_2y=c_2[/tex] has no solution if
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}[/tex]
Rewrite the equations
[tex]x+y=-4,\ cx-3y=18[/tex]
Insert the values for the no solution condition
[tex]\Rightarrow \dfrac{1}{c}=\dfrac{1}{-3}\\\\\Rightarrow c=-3[/tex]
Therefore, for c=-3, the system of linear equation ha no solution.
