How to graph system of equation
y=-2x+1
y=x-5
what does the solution mean to this problem?

Alright. So, we need to apply the substitution method.

y+5 = x - 5
         +5

y+5 = x

x = y+5            Now we have our value for x

Plug in the value for x, then solve.

y = -2(y+5) + 1

Distributive property

y = -2*y + -2*5 + 1
y = -2y + -10 + 1
y = -2y + -9

y+2y = -2y + -9
      +2y

3y = -9

3y/3 = -9/3
y = -3

Here, we know that y = -3

Now, apply it into an equation to solve for x.

-3+5 = x - 5
           +5

2 = x

Now we know that

x = 2

y = -3