Question

x+y=5
x-3y=3

Answer 1

I am not sure what you are aiming for. Mainly because you have not stated if this is an "and" , "or" equation.
Hope this helps.

Problem:
Solve x+y=5;x−3y=3
Steps:
I will try to solve your system of equations.
x+y=5;x−3y=3
Step: Solve x+y=5 for x:
x+y+−y=5+−y(Add -y to both sides)
x=−y+5
Step: Substitute (−y+5) for x in x−3y=3:
x−3y=3
−y+5−3y=3
−4y+5=3(Simplify both sides of the equation)
−4y+5+−5=3+−5(Add -5 to both sides)
−4y=−2
−4y
−4
=
−2
−4
(Divide both sides by -4)
y=
1
2
Step: Substitute (
1
2
) for y in x=−y+5:
x=−y+5
x=−
1
2
+5
x=
9
2
(Simplify both sides of the equation)
Answer:
x=9/2

and y= 1/2

Answer 2

a little less work would be to note that if you subtract one equation from the other, the x's disappear:

x+y=5
x-3y=3

4y = 2
y = 1/2

Then use that value of y in either equation to get x.