Question

Solve by elimination

5x+4y = 12
3x - 3y = 18

Please help solve and provide steps.

Answer 1

First you solve for y.
5x+ y= 12 so Y= 12-5x
And plug it into the next equation
3x- 3(12-5x) = 18
Distribute
3x-36+15x=18
Add 36 to both sides
3x+ 15x= 54
18x= 54 ... divide
x= 3
And you can plug in x to solve for Y
5(3) + y = 12
15+ y = 12 ...subtract 15 from both sides
y= -3

Answer 2

5x + 4y = 12 ⇒ 3(5x + 4y = 12) ⇒ 15x + 12y = 36

3x - 3y = 18 ⇒ 4(3x - 3y = 18) ⇒ 12x - 12y = 72

27x = 108

`(27x)/(27)` =
`(108)/(27)`

x = 4

5x + 4y = 12 ⇒ 5(4) + 4y = 12 ⇒ 20 + 4y = 12 ⇒ 4y = -8 ⇒ y = -2

Answer: x = 4, y = -2