To solve the system of equations, we can use the method of elimination. Multiply the second equation by -2 to eliminate x, and then add the two equations together. Simplify the equation and solve for y, then substitute that value back into one of the original equations to find x. The correct solution is x = -9 and y = 18.
Step-by-step explanation:
To solve the system of equations, we can use the method of elimination. We need to eliminate one of the variables by multiplying one of the equations by a constant, so that the coefficients of that variable will cancel out when we add the two equations together.
In this case, we can multiply the second equation by -2 to eliminate x. When we do that, we get:
6x + 5y = 36
-12x - 8y = -36
Now, we can add the two equations together:
-12x - 8y + 6x + 5y = -36 + 36
-6x - 3y = 0
Simplifying, we get:
-6x - 3y = 0
Now, we can solve this equation for y:
-3y = 6x
y = -2x
Now, we can substitute this value of y into one of the original equations, for example:
6x + 5(-2x) = 36
6x - 10x = 36
-4x = 36
x = -9
Finally, we can substitute this value of x into one of the original equations to find y:
6(-9) + 5y = 36
-54 + 5y = 36
5y = 90
y = 18
Therefore, the correct solution to the system of equations is x = -9 and y = 18.