Final answer:
To solve the system of equations -3x + 2y = 8 and -6x + 7y = -8, use the method of substitution. The solution is x = -8 and y = -8.
Step-by-step explanation:
To solve the system of equations -3x + 2y = 8 and -6x + 7y = -8, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve one of the equations for one variable. From the first equation, we can solve for x: -3x = -2y + 8, x = (2y - 8)/3.
Step 2: Substitute the value of x into the other equation. Substitute (2y - 8)/3 for x in the second equation: -6((2y - 8)/3) + 7y = -8.
Step 3: Solve the equation for y. Simplify and solve for y: -12y + 48 + 21y = -24, 9y = -72, y = -8.
Step 4: Substitute the value of y back into the first equation to solve for x. Substitute -8 for y in -3x + 2y = 8: -3x + 2(-8) = 8, -3x - 16 = 8, -3x = 24, x = -8.
The solution to the system of equations is x = -8 and y = -8.