To find the solution of the system of equations:
1. 6x + 8y = -8
2. x + 4y = 4
You can use the method of substitution or elimination. Let's use the elimination method:
Multiply equation (2) by 6 to make the coefficients of x in both equations equal:
2. 6x + 24y = 24
Now, subtract equation (1) from this modified equation (2):
(6x + 24y) - (6x + 8y) = 24 - (-8)
This simplifies to:
16y = 32
Now, divide both sides by 16 to solve for y:
y = 32 / 16
y = 2
Now that we have the value of y, we can substitute it back into equation (2) to solve for x:
x + 4y = 4
x + 4(2) = 4
x + 8 = 4
Subtract 8 from both sides:
x = 4 - 8
x = -4
So, the solution to the system of equations is:
x = -4
y = 2