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18 March, 09:28

Solve the equations using substitution

7x-2y=3

14x+y=14

+5
Answers (1)
  1. 18 March, 09:44
    0
    x = 31/35, y = 8/5

    Step-by-step explanation:

    Solve the following system:

    {7 x - 2 y = 3

    14 x + y = 14

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

    In the second equation, look to solve for y:

    {7 x - 2 y = 3

    14 x + y = 14

    Hint: | Solve for y.

    Subtract 14 x from both sides:

    {7 x - 2 y = 3

    y = 14 - 14 x

    Hint: | Perform a substitution.

    Substitute y = 14 - 14 x into the first equation:

    {7 x - 2 (14 - 14 x) = 3

    y = 14 - 14 x

    Hint: | Expand the left hand side of the equation 7 x - 2 (14 - 14 x) = 3.

    7 x - 2 (14 - 14 x) = (28 x - 28) + 7 x = 35 x - 28:

    {35 x - 28 = 3

    y = 14 - 14 x

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

    In the first equation, look to solve for x:

    {35 x - 28 = 3

    y = 14 - 14 x

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

    Add 28 to both sides:

    {35 x = 31

    y = 14 - 14 x

    Hint: | Solve for x.

    Divide both sides by 35:

    {x = 31/35

    y = 14 - 14 x

    Hint: | Perform a back substitution.

    Substitute x = 31/35 into the second equation:

    Answer: {x = 31/35, y = 8/5
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