Question

Solve the system of equations.

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

(1 point)

(8,-3)
(4,-7)
(18, 7)
(14, 3)

Answer 1

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

Given equations:
1) 3x - 4y = 40
2) 5x - 5y = 55

We need to eliminate one of the variables. Let's multiply the first equation by 5 and the second equation by 4:
1) 15x - 20y = 200
2) 20x - 20y = 220

Now, let's subtract the second equation from the first equation:
15x - 20y - 20x + 20y = 200 - 220
-5x = -20
x = 4

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation 1:
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, which corresponds to the point (4, -7). So the answer is:
(4, -7)