Math

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

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  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

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