Solve by substitution {x-4y=22} and {4x-5y=22}

X - 4y = 22
Add 4y to each side
x = 22 + 4y

Now replace x with 22 + 4y in the second equation.
4(22 + 4y) - 5y = 22
Distribute.
88 + 16y - 5y = 22
Simplify.
88 + 11y = 22
Subtract 88 from each side.
11y = -66
Divide by 11.
y = -6

Plug in -6 for y in an earlier equation and solve for x.
x-4(-6)=22
Negative 4 times negative 6 = 24 (the negatives cancel)
x+24=22
Subtract 24 from each side.
x = -2