- 4x + y = 6
- 5x - y = 21
To do this we need to rearrange one of the equations. It doesn't matter which one you choose to rearrange but I will choose the first.
- 4x + y = 6
Let's add '4x' to both sides of the equation so that we have an equation in the form
y = ......
- 4x + 4x + y = 6 + 4x
y = 6 + 4x
And so now we know what 'y' equals. We can substitute this into the second equation to help us find out what 'x' equals.
- 5x - y = 21
- 5x - (6 + 4x) = 21
- 5x - 6 - 4x = 21
- 9x - 6 = 21
- 9x - 6 + 6 = 21 + 6
- 9x = 27
x = 27/(-9)
x = - 3
And so now we know what 'x' equals we can find out what 'y' equals by substituting x = - 3 into either of the original two equations.
I will use the equation, - 4x + y = 6 , but you should also get the same answer if you choose the equation, - 5x - y = 21 (a good way of checking if your answer is correct is to put the values for 'x' or 'y' into both equations and seeing if they both come up with the same answer 
)
So,
- 4x + y = 6
- 4*(- 3) + y = 6
12 + y = 6
12 - 12 + y = 6 - 12
y = - 6
This means that the solution to your set of equations is x = - 3 and y = - 6.