Solve the systems of equations x+8y=2 2y-x=18

We pick one of the equations and isolate the y on one side.
x+8y = 22y=18+x
We express the equation 2 in terms of y, dividing it by 2.
x+8y = 2y = (18+x)/2
which is the same than
x+8y = 2y = 9 + x/2
We plug the y into the first expression, we find :
x + 8*(9+ x/2) = 2x + 72 + 8x/2 = 2x +4x = 2 - 725x = - 70x = -70/5 = - 14
We now have found that x = - 14
Lets plug it into the second equation to find y
y = 9 - 14/2y = 9 - 7y = 2
The sytem of two equations is solved!
y= 2 and x = - 14