3x−4y=40
5x−5y=55
To solve this system of equations, we can use either the substitution or elimination method. Let's use the elimination method.
First, let's multiply the first equation by 5 and the second equation by 4 to make the coefficients of y opposite:
15x - 20y = 200
20x - 20y = 220
Now, let's subtract the second equation from the first:
15x - 20y - 20x + 20y = 200 - 220
-5x = -20
x = 4
Now that we have found x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
3(4) - 4y = 40
12 - 4y = 40
-4y = 28
y = -7
Therefore, the solution to the system of equations is x = 4 and y = -7.