Answer:
[tex]x = -2\\y = -4[/tex]
Step-by-step explanation:
Question
[tex]\left \{ {{-2x + 2y = -4} \atop {3x + 3y = -18}} \right.[/tex]
Multiply throughout the equation to eliminate a variable:
[tex]-2x + 2y = -4[/tex] becomes [tex]-6x + 6y = -12[/tex] when multiplied by 3
[tex]3x + 3y = -18[/tex] becomes [tex]6x + 6y = -36[/tex] when multiplied by 2
Then add the values of the variables together:
[tex]-6x + 6x = 0\\6y + 6y = 12y \\-12 - 36 = -48[/tex]
And a new equation forms:
[tex]0 + 12y = -48[/tex]
[tex]y = -4[/tex]
Plug in [tex]y[/tex] to any of the previous equations to solve for [tex]x[/tex] :
[tex]-2x + 2y = -4[/tex]
[tex]-2x + 2(-4) = -4[/tex]
[tex]-2x - 8 = -4[/tex]
[tex]-2x = 4[/tex]
[tex]x = -2[/tex]
