Use substitution to solve

y=-2x+1

y=x-5

Substitute the y=x-5 into the first equation.

So y=-2x+1 becomes x-5=-2x+1.

Solve for x by isolating x variable terms on one side and integers on the other.

X+2x=1+5

3x=6

X=2

Then plug x=2 into y=x-5

Y=2-5=-3

So x=2, y=-3