If y=4-4x, then we can replace the color(blue)(y) in 4x+color(blue)(y)=4 with 4-4x:
4x+(4-4x)=4
Solve for x
4x+4-4x=4
subtract 4 on both sides
4x-4x=0
0x=0
x=oo
color(white)(0)
Let's try solving for y now.
We need to isolate x:
4x+y=4
4x=4-y
x=(4-y)/4
Now, let's replace color(blue)(x) with (4-y)/4 in y=4-4color(blue)(x)
y=4-cancel(4)(color(black)((4-y)/cancel(4)))
y=4-4-y
0y=0
y=oo
The reason x and y both equal oo is that any number, multiplied by 0, equals 0. So, x can equal -500, 8/19, or 9.01xx10^13, and still equal 0, thus making the equation true. The same fact also applies for y.
Both x and y equal all real numbers
