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8 March, 18:48

What is the solution to the system of equations y=-1/3x+9 and y=2/3x+12

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  1. 8 March, 19:40
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    {x = - 3, y = 10

    Step-by-step explanation:

    Solve the following system:

    {y = 9 - x/3 | (equation 1)

    {y = (2 x) / 3 + 12 | (equation 2)

    Express the system in standard form:

    {x/3 + y = 9 | (equation 1)

    { - (2 x) / 3 + y = 12 | (equation 2)

    Swap equation 1 with equation 2:

    { - (2 x) / 3 + y = 12 | (equation 1)

    {x/3 + y = 9 | (equation 2)

    Add 1/2 * (equation 1) to equation 2:

    { - (2 x) / 3 + y = 12 | (equation 1)

    {0 x + (3 y) / 2 = 15 | (equation 2)

    Multiply equation 1 by 3:

    { - (2 x) + 3 y = 36 | (equation 1)

    {0 x + (3 y) / 2 = 15 | (equation 2)

    Multiply equation 2 by 2/3:

    { - (2 x) + 3 y = 36 | (equation 1)

    {0 x+y = 10 | (equation 2)

    Subtract 3 * (equation 2) from equation 1:

    { - (2 x) + 0 y = 6 | (equation 1)

    {0 x+y = 10 | (equation 2)

    Divide equation 1 by - 2:

    {x+0 y = - 3 | (equation 1)

    {0 x+y = 10 | (equation 2)

    Collect results:

    Answer: {x = - 3, y = 10
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