Question

Solve the system of equations by elimination.

Answer 1

x = -4 and y = 0

Explanation:

We can solve the system of equations by substitution or elimination. Here, we will use the substitution method.

First, we will solve for y in the first equation:

y = -16 - 4x

Next, we will substitute this expression for y into the second equation:

2x - 3y = -8

2x - 3(-16 - 4x) = -8

2x + 48 + 12x = -8

14x = -56

x = -4

Now that we have found the value of x, we can substitute it back into the first equation to solve for y:

y = -16 - 4x

y = -16 - 4(-4)

y = -16 + 16

y = 0

Therefore, the solution to the system of equations is x = -4 and y = 0.

Answer 2

(- 4, 0 )

Explanation:

4x + y = - 16 → (1)

2x - 3y = - 8 → (2)

multiplying (1) by 3 and adding to (2) will eliminate y

12x + 3y = - 48 → (3)

add (2) and (3) term by term to eliminate y

(2x + 12x) + (- 3y + 3y) = - 8 - 48

14x + 0 = - 56

14x = - 56 ( divide both sides by 14 )

x = - 4

substitute x = - 4 into either of the 2 equations and solve for x

substituting into (1)

4(- 4) + y = - 16

- 16 + y = - 16 ( add 16 to both sides )

y = 0

solution is (- 4, 0 )