SOLUTION: Solve the system of equations by the elimination method. (If the system is dependent, let y = c and enter a general solution in terms of c. If there is no solution, enter NO SOLUTI

Question 1130421: Solve the system of equations by the elimination method. (If the system is dependent, let y = c and enter a general solution in terms of c. If there is no solution, enter NO SOLUTION.)
{4x+ 7y= 28
5x−4y=−16
(x, y) =
Answer by ikleyn(53763) (Show Source): You can put this solution on YOUR website!
.

4x + 7y =  28        (1)
5x - 4y = -16        (2)


Multiply eq(1) by 5 (both sides).  Multiply eq(2) by 4 (both sides).  You will get


20x + 35y =  140      (3)
20x - 16y = -64       (4)


Subtract eq(4) from eq(2).  The terms  " 20x " will cancel each other, and you will get a single equation for the unknown "y" only.

It is how the Elimination method works.


      35y - (-16y) = 140 - (-64)

      51y = 204

        y = 204/51 = 4.


Now substitute the value y= 4 into eq(1). You will get


     4x + 7*4 = 28

     4x = 28 - 28 = 0

      x = 0.


Answer.  x= 0;  y= 4.


CHECK.  Check the solution on your own by substituting the ontained values into each of the two given equations.

Solved.

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