Question

2x-3y=31
3x+2y=1

Solve by elimination method

Answer 1

2x - 3y = 31 ⇒ 6x - 9y = 93
3x + 2y = 1 ⇒ 6x + 4y = 2
-5y = 91
-5 -5
y = -18 1/5
2x - 3(-18 1/5) = 31
2x + 54 3/5 = 31
- 54 3/5 - 54 3/5
2x = -24 3/5
2 2
x = -12 3/10
(x, y) = (-12 3/10, -18 1/5)

Answer 2

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)}