Final answer:
The solution to the system of equations 5x-4y=33 and 3x-3y=24 is found using the elimination method. By aligning the coefficients of y and eliminating it, we find that x=1. Substituting x=1 back into one of the equations gives us y=-7, which completes our solution.
Step-by-step explanation:
To solve the system of equations 5x-4y=33 and 3x-3y=24 using the elimination method, we aim to eliminate one of the variables by making the coefficients of one variable equal in both equations. We can multiply the second equation by 4/3 to have a coefficient of -4 for y, which will match the coefficient of y in the first equation. Now, we can multiply the second equation by 4/3 to align the coefficients of y. Doing so transforms the second equation into:
4x - 4y = 32 (after multiplying 3x-3y=24 by 4/3)
We can now subtract this new equation from the first equation to eliminate y:
- 5x - 4y = 33 (original first equation)
- 4x - 4y = 32 (modified second equation)
Subtracting we get:
x = 1
Now substitute x=1 back into one of the original equations to find y. We'll use the first equation:
5(1) - 4y = 33
5 - 4y = 33
-4y = 33 - 5
-4y = 28
y = -7
Therefore, the solution to the system of equations is x=1 and y=-7.