Question

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

Answer 1

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

Answer:
x = 5; y = 2

(5, 2)