Question

Solve the system of equations:

-12x + 4y = -1
8x + 2y = 3

A. (x, y) = (1, -3)
B. (x, y) = (-1, 1)
C. (x, y) = (-2, 2)
D. (x, y) = (3, 0)

Answer 1

To solve the system of equations, multiply the first equation by 2 and the second equation by 3 to eliminate the y variable. Add the two equations together to eliminate the x variable. Divide both sides of the equation by 14 to solve for y. Substitute the value of y back into either of the original equations to solve for x. The solution is (x, y) = (-1/12, 1/2).

Step-by-step explanation:

To solve the given system of equations:

-12x + 4y = -1

8x + 2y = 3

1. Start by multiplying the first equation by 2 and the second equation by 3 to eliminate the y variable.

-24x + 8y = -2

24x + 6y = 9

2. Add the two equations together to eliminate the x variable.

14y = 7

3. Divide both sides of the equation by 14 to solve for y.

y = 1/2

4. Substitute the value of y back into either of the original equations to solve for x.

-12x + 4(1/2) = -1

-12x + 2 = -1

-12x = 1

x = -1/12

Therefore, the solution to the system of equations is (x, y) = (-1/12, 1/2).