Solve the system of linear equations.

y=x-5

y=-2x+1

x-5=-2x+1

3x=6

x=2

y=x-5=2-5=-3

y=-3

The solution is (2; - 3)

I solved this one by substitution. When you are solving for two equations you can do this.

y=x-5

y=-2x+1

substitute the y in one of the equations to find x

x-5=-2x+1

x=-2x+6

3x=6

x=2

then you plug in that number to one of the equations

y=2-5

y=-3