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This is a simultaneous equation.
We want to get an equation that has just x's or just y's so that it can be solved. You need to have a look at both equations to work out which would be the easiest way.
In this case we are already told that y=5x+1 so all we have to do is substitute this into the equation.
So 8x + 2y = -2 becomes 8x + 2(5x + 1) = -2
So, 8x + 10x + 2 = -2
18x + 2 = -2
We now need to get x on one side of the equation and the number on the other.
As in all equations we must do the same thing on both sides
18x + 2 - 2 = -2 -2
18x = -4
x = -4/18 = -2/9
We now put this value of x back into one of the equations to find y - look for which one looks the simplest.
y = 5x+1 = -10/9 + 1 = -1/9
So the answer is that x=-2/9 and y= -1/9