Solve the system of equations.

3x−4y=40

5x−5y=55

Responses

(8,−3)
open paren 8 comma negative 3 close paren - no response given

(18, 7)
(18, 7)
- no response given

(14, 3)
(14, 3)
- no response given

(4,−7)
show your work

1 answer

First, let's isolate one variable in one of the equations. Let's multiply the first equation by 5 and the second one by 3 to make the coefficients of y the same:

15x - 20y = 200
15x - 15y = 165

Now we can subtract the second new equation from the first new equation:

15x - 20y - 15x + 15y = 200 - 165
-5y = 35
y = -7

Now, substitute y = -7 into one of the original equations to solve for x:

3x - 4(-7) = 40
3x + 28 = 40
3x = 12
x = 4

Therefore, the solution to the system of equations is (4, -7).