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, [tex]-2x+y=10[/tex] this can quite easily be manipulated to show [tex]y=10+2x[/tex].
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 [tex]4x-y=-14 \Rightarrow 4x-(10+2x)=-14[/tex] which can then be solved for x since there is only one variable [tex]4x-10-2x=-14 \Rightarrow 2x=-4 \Rightarrow x=-2[/tex] and then with our x solution we can work out our y solution by using the equation we manipulated [tex]y=10+2x = 10+(2 \times -2) = 10-4=6[/tex].
So the solution to these equations is x=-2 when y=6
