SOLUTION: Solve the system of equations using the substitution method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no s

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Question 68775: Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-4x + y = 8
2x + 3y = -1
Answer by rmromero(383)   (Show Source): You can put this solution on YOUR website!


Here are the Steps using Substition method

1. In either equation, solve for one variable in terms of the other.

     -4x + y = 8

           y = 4x + 8



2. Substitute 4x + 8 for y in the other equation. Solve x.

             2x + 3y = -1 

      2x + 3(4x + 8) = -1

       2x + 12x + 24 = -1

            14x + 24 = -1

                 14x = -25

                   x = -25/14 



3. Substitute the result from step 2 in either equation 2x + 3y = -1. 

   Solve for the other variable.

       -4x + y = 8 , x = -25/14

-4(-25/14) + y = 8

    100/14 + y = 8

             y = 12/14





4. Check the solution in both original equations.



             2x + 3y = -1, x = -25/14, y = 12/14

2(-25/14) + 3(12/14) = -1 

      -50/14 + 36/14 = -1

              -14/14 = -1

                  -1 = -1 ----------->True



             -4x + y = 8, x = -25/14, y = 12/14 

-4(-25/14) + (12/14) = 8

      100/14 + 12/14 = 8

              112/14 = 8

                   8 = 8  ----------->>True



There is a unique solution, (-25/14, 12/14)















 

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