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5 June, 17:04

How do you solve 2x-3y=-4 and x+3y=7 by substitution

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  1. 5 June, 17:22
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    x = 1, y = 2

    Step-by-step explanation:

    Solve the following system:

    {2 x - 3 y = - 4

    x + 3 y = 7

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

    In the second equation, look to solve for x:

    {2 x - 3 y = - 4

    x + 3 y = 7

    Hint: | Solve for x.

    Subtract 3 y from both sides:

    {2 x - 3 y = - 4

    x = 7 - 3 y

    Hint: | Perform a substitution.

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

    {2 (7 - 3 y) - 3 y = - 4

    x = 7 - 3 y

    Hint: | Expand the left hand side of the equation 2 (7 - 3 y) - 3 y = - 4.

    2 (7 - 3 y) - 3 y = (14 - 6 y) - 3 y = 14 - 9 y:

    {14 - 9 y = - 4

    x = 7 - 3 y

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

    In the first equation, look to solve for y:

    {14 - 9 y = - 4

    x = 7 - 3 y

    Hint: | Isolate terms with y to the left hand side.

    Subtract 14 from both sides:

    {-9 y = - 18

    x = 7 - 3 y

    Hint: | Solve for y.

    Divide both sides by - 9:

    {y = 2

    x = 7 - 3 y

    Hint: | Perform a back substitution.

    Substitute y = 2 into the second equation:

    {y = 2

    x = 1

    Hint: | Sort results.

    Collect results in alphabetical order:

    Answer: {x = 1, y = 2
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