Posted by **Sarah** on Tuesday, January 18, 2011 at 6:09pm.

Use linear combinations to solve the system of linear equations.

5x=4y-30

2x+3y+-12

- Math -
**helper**, Tuesday, January 18, 2011 at 6:49pm
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

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