So,
Let's eliminate the y's.
Multiply the first equation by 2
4x - 6y = 62
Multiply the second equation by 3
9x + 6y = 3
Add the two equations together
13x = 65
Divide both sides by 13
x = 5
Substitute in the second equation
3(5) + 2y = 1
15 + 2y = 1
Subtract 15 from both sides
2y = -14
Divide both sides by 2
y = -7
Check
3(5) + 2(-7) = 1
15 + -14 = 1
1 = 1 This checks.
2(5) - 3(-7) = 31
10 - -21 = 31
10 + 21 = 31
31 = 31 This also checks.
S = {(5,-7)}
