Question

Is there an ordered pair that is in the solution to both of these linear equations

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Answer 1

(- 4, 2 )

Explanation:

y = 3x + 14 → (1)

2x - 3y = - 14 → (2)

substitute y = 3x + 14 into (2)

2x - 3(3x + 14) = - 14 ← distribute parenthesis on left side and simplify

2x - 9x - 42 = - 14

- 7x - 42 = - 14 ( add 42 to both sides )

- 7x = 28 ( divide both sides by - 7 )

x = - 4

substitute x = - 4 into (1)

y = 3(- 4) + 14 = - 12 + 14 = 2

solution is (- 4, 2 )