Question

Identify the solution to the system of equations
{x=-2y-6 -3x-7y=18

Answer 1

(- 6, 0 )

Explanation:

x = -2y - 6 → (1)

- 3x - 7y = 18 → (2)

substitute x = - 2y - 6 into (2)

- 3(- 2y - 6) - 7y = 18 ← distribute parenthesis and simplify left side

6y + 18 - 7y = 18

- y + 18 = 18 ( subtract 18 from both sides )

- y = 0 , then

y = 0

substitute y = 0 into (1)

x = - 2(0) - 6 = 0 - 6 = - 6

solution is (- 6, 0 )

Answer 2

(x, y) = (-6, 0)

Explanation:

A system of equations is easily solved using a graphing calculator. The attached shows the solution to be ...

(x, y) = (-6, 0)

__

The first equation gives a convenient expression for substituting for x in the second equation:

-3(-2y -6) -7y = 18

18 -y = 18 . . . . . . . . simplify

y = 0 . . . . . . . . add y-18

x = -2(0) -6 = -6

The solution by substitution is (x, y) = (-6, 0).