Answer: the solution to the system of equations is x = 7 and y = 7.
Step-by-step explanation: To solve the system of equations:
Equation 1: -2x - 2y = -28
Equation 2: 2x + 4y = 42
We can use the method of elimination to find the values of x and y.
First, let's multiply Equation 1 by 2 to eliminate the x term:
Equation 1: -4x - 4y = -56
Equation 2: 2x + 4y = 42
Adding Equation 1 and Equation 2:
(-4x - 4y) + (2x + 4y) = -56 + 42
Simplifying the equation:
-2x = -14
Dividing both sides of the equation by -2:
x = 7
Now that we have the value of x, we can substitute it back into Equation 2 to find the value of y:
2(7) + 4y = 42
Simplifying the equation:
14 + 4y = 42
Subtracting 14 from both sides of the equation:
4y = 28
Dividing both sides of the equation by 4:
y = 7