Final answer:
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).