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15 October, 03:50

Solve the system of equations using the substitution method. {y=-3x+7x=-2y-16 Enter your answers in the boxes.

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  1. 15 October, 04:03
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    x = 6, y = - 11

    Step-by-step explanation using the substitution:

    Solve the following system:

    {y = 7 - 3 x

    {x = - 2 y - 16

    Hint: | Perform a substitution.

    Substitute y = 7 - 3 x into the second equation:

    {y = 7 - 3 x

    {x = - 2 (7 - 3 x) - 16

    Hint: | Expand the right hand side of the equation x = - 2 (7 - 3 x) - 16.

    -2 (7 - 3 x) - 16 = (6 x - 14) - 16 = 6 x - 30:

    {y = 7 - 3 x

    {x = 6 x - 30

    Hint: | Choose an equation and a variable to solve for.

    In the second equation, look to solve for x:

    {y = 7 - 3 x

    {x = 6 x - 30

    Hint: | Isolate x to the left hand side.

    Subtract 6 x from both sides:

    {y = 7 - 3 x

    {-5 x = - 30

    Hint: | Solve for x.

    Divide both sides by - 5:

    {y = 7 - 3 x

    {x = 6

    Hint: | Perform a back substitution.

    Substitute x = 6 into the first equation:

    {y = - 11

    {x = 6

    Hint: | Sort results.

    Collect results in alphabetical order:

    Answer: x = 6, y = - 11
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