If y=4-4xy=4−4x, then we can replace the color(blue)(y)y in 4x+color(blue)(y)=44x+y=4 with 4-4x4−4x:
4x+(4-4x)=44x+(4−4x)=4
Solve for xx
4x+4-4x=44x+4−4x=4
subtract 44 on both sides
4x-4x=04x−4x=0
0x=00x=0
x=oox=∞
color(white)(0)0
Let's try solving for yy now.
We need to isolate xx:
4x+y=44x+y=4
4x=4-y4x=4−y
x=(4-y)/4x=4−y4
Now, let's replace color(blue)(x)x with (4-y)/44−y4 in y=4-4color(blue)(x)y=4−4x
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
