Because the equations are arranged so that corresponding terms are matching, we can use elimination and add each corresponding term.
7x+3y=8
6x−3y=5
+7x6x3y−3y85
13x=13
x=1
Substituting x into either equation,
7x+3y=8
7(1)+3y=8
7+3y=8
3y=1
y=31
Finally,
x−y=1−31
=32
Although elimination is efficient, we can also use substitution to eliminate a variable. Note that the 3y term is present in both equations.
7x+3y=8
6x−3y=5
Solving for 3y in the first equation,
7x+3y=8
3y=8−7x
Substituting this value into the second equation,
6x−3y=5
6x−(8−7x)=5
6x−8+7x=5
13x=13
x=1
Substituting x into either equation,
7x+3y=8
7(1)+3y=8
7+3y=8
3y=1
Finally,
x−y=1−31
=32