X - y = 3

x + 3y = 9

X - y = 3 is the same as x=3+y

3+y+3y = 9

3+4y=9

4y=9-3

4y=6

y=6/4

y=3/2

x - (3/2) = 3

x=3 + (3/2)

x=6/2+3/2

x=9/2

Solve for one of the variables in the first equation (in this case, I will solve for X):

X = Y + 3

Then use that value of X in the second equation to solve for Y:

X + 3Y = 9

(Y + 3) + 3Y = 9

4Y + 3 = 9

4Y = 6

Y = 1.5

Use the value of Y we just found in the X equation we created:

X = Y + 3

X = 1.5 + 3

X = 4.5

Therefore X = 4.5 or 9/2 and Y = 1.5 or 3/2.