6x – 7y = 16 2x + 7y = 24 (2, 1) (2, 0) (5, 2) (4, –5)

6x – 7y = 16
2x + 7y = 24

This system is easily solvable by the elimination method as the y-terms are opposites of each other. You may add the two equations together and they will cancel out.

    6x – 7y = 16 
    2x + 7y = 24
+
    8x –  0 = 40
           8x = 40
             x = 5

Substitute 5 for x into either of the above equation and solve algebraically for y.

       2x + 7y = 24
    2(5) + 7y = 24
      10 + 7y = 24
              7y = 14
                y = 2

Check work by plugging both x- and y-values into each original equation.

    6x – 7y = 16  =>  6(5) – 7(2) = 16  =>  30 – 14 = 16
    2x + 7y = 24  =>  2(5) + 7(2) = 24  =>  10 + 14 = 24

x = 5; y = 2

(5, 2)