Answer:
[tex]\boxed{\sf x=-2}[/tex]
[tex]\boxed{\sf y=-4}[/tex]
Step-by-step explanation:
First, Let's solve for x in -2x+2y=-4:
[tex]\sf -2x+2y=-4[/tex]
Subtract 2y from both sides:
[tex]\sf -2x+2y-2y=-4-2y[/tex]
[tex]\sf -2x=-4-2y[/tex]
Divide both sides by -2:
[tex]\sf \cfrac{-2x}{-2}=-\cfrac{4}{-2}-\cfrac{2y}{-2}[/tex]
[tex]\bold{ x=y+2}[/tex]
Now, we'll substitute x=y+2 to 3x+3y=-18:
[tex]\sf 3x+3y=-18[/tex]
→ let x=2+y
[tex]\sf 3\bold{(2+y)}+3y=-18[/tex]
Simplify:
[tex]\sf 6+6y=-18[/tex]
Now, let's solve for y in 6+6y=-18
[tex]\sf 6+6y=-18[/tex]
Subtract 6 from both sides:
[tex]\sf 6+6y-6=-18-6[/tex]
[tex]\sf 6y=-24[/tex]
Divide both sides by 6:
[tex]\sf \cfrac{6y}{6}=\cfrac{-24}{6}[/tex]
[tex]\bold{ y=-4}[/tex]
Now, substitute y=-4 into x=2+y:
[tex]\sf x=2+y[/tex]
→ let y = -4
[tex]\sf x=2+\bold{-4}[/tex]
[tex]\bold{x=-2}[/tex]
Therefore, x=-2 and y=-4.
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