4. Solve the system of two equations.

Question

3x - 4y = 40
5x - 5y = 55

Answer 1

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

First, we'll multiply the first equation by 5 and the second equation by 4 to make the coefficients of y in both equations the same:

(5)(3x - 4y) = 5(40)
(4)(5x - 5y) = 4(55)
15x - 20y = 200
20x - 20y = 220

Now, subtract the second equation from the first:

15x - 20y - 20x + 20y = 200 - 220
-5x = -20
x = 4

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

3x - 4y = 40
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.