Question

I need to know the solution to this

Answer 1

There are two ways to do this but the way I prefer is to make one of the equations in terms of one variable and then 'plug this in' to the second equation. I will demonstrate

Look at equation 1, $-2x+y=10$ this can quite easily be manipulated to show $y=10+2x$.

Then because there is a y in the second equation (and both equations are simultaneous) we can 'plug in' our new equation where y is in the second one $4x-y=-14 \Rightarrow 4x-(10+2x)=-14$ which can then be solved for x since there is only one variable $4x-10-2x=-14 \Rightarrow 2x=-4 \Rightarrow x=-2$ and then with our x solution we can work out our y solution by using the equation we manipulated $y=10+2x = 10+(2 \times -2) = 10-4=6$.

So the solution to these equations is x=-2 when y=6