Question

Given the system of equations:

6x + 2y = −6
3x − 4y = −18

Solve for (x, y) using elimination.

Answer 1

Multiplying the second equation by 2, we get:

6x - 8y = -36

Adding this equation to the first equation, we eliminate y:

6x + 2y + 6x - 8y = -6 - 36

Simplifying:

12x = -42

Dividing by 12:

x = -7/2

Substituting this value into either of the original equations (we'll use the first one):

6(-7/2) + 2y = -6

Simplifying:

-21 + 2y = -6

Adding 21 to both sides:

2y = 15

Dividing by 2:

y = 7.5

Therefore, the solution is (x, y) = (-7/2, 7.5).

Answer 2

Wrong answer by the bot

6x + 2y = −6 -----> double this: 12x + 4y = -12
3x − 4y = −18

add them:
15x = -30
x = -2

sub into first:
6(-2) + 2y = -6
2y = 6
y = 3
so x= -2 and y = 3

Answer 3

You are correct, thank you for catching that error. The solution is indeed (x, y) = (-2, 3).