SOLUTION: Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answe

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Question 68776: Solve the system of equations using the addition (elimination) 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.”
5x + y = -2
4x + 7y = 2
Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!
Elimination Method
1. Add or subtract the given equations to eliminate one variable.
   y term may be eliminated, if the first equation is multiply by -7
      7(5x + y = -2)
        4x + 7y = 2
      _____________

      -35x - 7y = 14
        4x + 7y = 2
      _______________
           -31x = 16
              x = -16/31

2. Replace the value of the known variable in one of the original equations
   to find the value of the unknown variable.

        4x + 7y = 2, x = -16/31
 4(-16/31) + 7y = 2
    -64/31 + 7y = 2
             7y = 126/31
              y = 18/31

  
4. Check the solution in both original equation.
           5x + y = -2, x = -16/31, y = 18/31
5(-16/31) + 18/31 = -2
   -80/31 + 18/31 = -2
           -62/21 = -2
              -2  = -2  ----------->> True

           4x + 7y = 2, x = -16/31, y = 18/31
4(-16/31)+7(18/31) = 2
   -64/31 + 126/31 = 2
             62/31 = 2
                 2 = 2  ------------>> True

Check the graph

graph+%28300%2C+300%2C+-5%2C+5%2C+-3%2C+7%2C+%28-5%29x-2%2C+%28-4%2F7%29x%2B2%2F7%29

There is a unique solution, (-16/31, 18,31)