To solve these equations, our aim is to find a value of x and a value of y that satisfy both equations at the same time. By satisfy we mean, if we plug our values in for x and y then the left hand side and right hand side of each equation will equal eachother.
First to find x and y we must try and eliminate either x or y to find the other.
Lets try and eliminate x.
We can write equation (2) with x as the subject by subtracting 4y from both sides, like so:
x=13-4y
Now we can substitute this into equation (1) to eliminate x giving:
5(13-4y) + 2y = 20
Expanding the brackets gives
65 - 20y + 2y = 20
Now we collect all the y's onto one side and the constants onto the other giving:
45 = 18y
Then divide through by 18 to give y=5/2
Now we substitute this into either equation (1) or (2) for y to find x.
With (1) : 5x + 2(5/2) = 20, 5x = 15, x=3
With (2) : x + 4(5/2) = 13, 5x=15, x=3
So our solution is x=3, y=5/2. It isn't necessary to show x's value with both equations but it can be useful to check your answer is correct!