Solve for the system of linear equations x+y=4 2x+3y=0

X+y=4
2x+3y=0
x=4-y
2(4-y)+3y=0
8-2y+3y=0
8+y=0
y=-8
x+(-8)=4
x-8=4
x=12

Solve x+y=4 for x
x+y+-y=4+-y(add -y to both sides)
x=-y+4
substitute -y+4 for x in 2x+3y=0
2x+3y=0
2(-y+4)+3y=0
y+8=0(simplify both sides of the equation)
y+8+-8=0+-8(add -8 to both sides)
y=-8
substitute -8 for y in x=-y+4:
x=-y+4
x=-(-8)+4
x=12(simplify both sides of the equation)
answer is x=12 and y=-8