Solve using the elimination method.

4x+3y=-45.5
-5x+8y=-43

Multiply first equation by 5 and second by 4.

Add the two equations to eliminate x and solve for y. Insert y value to find x in one equation and then put both values into the second as a check.

To solve this system of equations using the elimination method, we need to eliminate one variable. Let's start by eliminating the x-variable.

To do that, we will multiply the first equation by 5 and the second equation by 4 so that the coefficients of x in both equations will be equal and opposite. This will allow us to add the two equations together, eliminating the x-variable.

Multiply the first equation by 5:
5(4x + 3y) = 5(-45.5)
20x + 15y = -227.5

Multiply the second equation by 4:
4(-5x + 8y) = 4(-43)
-20x + 32y = -172

Now, let's add the two equations together:

(20x + 15y) + (-20x + 32y) = -227.5 + (-172)

Simplifying the equation:

20x - 20x + 15y + 32y = -227.5 - 172
47y = -399.5

Divide both sides of the equation by 47:

(47y) / 47 = (-399.5) / 47
y = -8.5

Now we have found the value of y. To find x, we will substitute the value of y back into one of the original equations. Let's use the first equation:

4x + 3(-8.5) = -45.5
4x - 25.5 = -45.5
4x = -45.5 + 25.5
4x = -20
x = -20 / 4
x = -5

Therefore, the solution to the system of equations is x = -5 and y = -8.5.