Solve the set of equations
x-y=4
2x+y=9

X - y = 4 (1)
2x + y = 9 (2)
We need to solve for x and y.

Let's find the algebraic value of x using the equation (1):
x-y = 4
add y in both sides
x-y+y = 4+y
x = 4+y

Now let's using this value instead of x in the equation (2):
2x + y = 9
2(4+y) + y = 9
8 + 2y + y = 9
3y + 8 = 9
Subtract 8 from both sides
3y + 8 - 8 = 9 - 8
3y = 1
divide both sides by 3
(3y)/3 = 1/3
y=1/3

Let's use the value of y to find the value x using the equation (1)
x - y = 4
x = y+4
x = 1/3 + 4
x = 13/3

So x = 13/3 and y = 1/3

Let's recheck the answers (very important):
x - y = 13/3 - 1/3 = 12/3 = 4 (correct)
2x + y = 2*(13/3) + 1/3 = 26/3 + 1/3 = 27/3 = 9 (correct)
The answer has been approved.

Hope this helps! :D