Question

Find the ordered pair that is a member of both -6x + 3y = 84 and

-6x - 3y = 24 or indicate if it does not exist or there are infinite
possibilities.

Answer 1

(- 9, 10 )

Explanation:

Solve the equations simultaneously to find solution to both

- 6x + 3y = 84 → (1)

- 6x - 3y = 24 → (2)

add (1) and (2) term by term to eliminate y

- 12x + 0 = 108

- 12x = 108 ( divide both sides by - 12 )

x = - 9

substitute x = - 9 into either of the 2 equations and solve for y

substituting into (1)

- 6(- 9) + 3y = 84

54 + 3y = 84 ( subtract 54 from both sides )

3y = 30 ( divide both sides by 3 )

y = 10

solution is (- 9, 10 )