Question

Use linear combinations to solve the system of linear equations.
5x=4y-30
2x+3y+-12

Answer 1

5x = 4y - 30
2x + 3y +-12

(1) 5x - 4y = -30
(2) 2x + 3y = 12

multiply (1) by 3(5x - 4y = -30)
(1) 15x + 12y = -90
multiply (2) by 4(2x + 3y = 12)
(2) 8x + 12y = 48

ADD two new equations
(1) 15x + 12y = -90
(2) 8x + 12y = 48
23x + 0 = -42
23x = -42
x = -42/23

substitute x = -42/23 in 2x + 3y = 12
to find y

(2) 2x + 3y = 12
2(-42/23) + 3y = 12
-84/23 + 3y = 12
3y = 12 + 84/23
3y = 276/23 + 84/23
3y = 360/23
y = 360/23 * 1/3
y = 360/69
y = 120/23

x = -42/23,
y = 120/23