Final answer:
To solve the system of equations -8x - 9y = 14 and 4(2x - 2y) = -12, you can start by simplifying the second equation and eliminating the x terms. Then, add the equations and simplify further. Solve the resulting equation to find the value of x. Substitute the values of x and y back into one of the original equations to check the solution.
Step-by-step explanation:
To solve the system of equations:
-8x - 9y = 14
4(2x - 2y) = -12
First, let's simplify the second equation:
8x - 8y = -12
Next, we can eliminate the x terms by multiplying the first equation by 8:
-64x - 72y = 112
Then, we can add the two equations:
-64x - 72y + 8x - 8y = 112 - 12
-56x - 80y = 100
Simplifying further:
-7x - 10y = 12.5
To solve for y, we can multiply the first equation by 10:
-80x - 90y = 140
By adding the two equations:
-80x - 90y -7x - 10y = 140 + 12.5
-87x - 100y = 152.5
By solving this new equation, we can find the value of x. Once you have the values of x and y, you can substitute them back into one of the original equations to check if they satisfy the system of equations.