To find the values of x and y that satisfy the system of equations:
1. x + 3y = -4
2. -x + 5y = -8
You can use the method of substitution or elimination. I'll use the elimination method.
First, add the two equations together to eliminate x:
(x + 3y) + (-x + 5y) = (-4) + (-8)
This simplifies to:
8y = -12
Now, divide both sides by 8 to solve for y:
y = -12 / 8
y = -3/2
Now that you have found the value of y, you can substitute it back into one of the original equations to solve for x. Let's use the first equation:
x + 3(-3/2) = -4
x - (9/2) = -4
To isolate x, add (9/2) to both sides:
x = -4 + (9/2)
x = (-8/2) + (9/2)
x = (1/2)
So, the solution to the system of equations is:
x = 1/2
y = -3/2