Solve the system of equations.

Question

3x−4y=40
5x−5y=55 (1 point)
Responses

(14, 3)
left parenthesis 14 comma 3 right parenthesis

(8,−3)
left parenthesis 8 comma negative 3 right parenthesis

(18, 7)
left parenthesis 18 comma 7 right parenthesis

(4,−7)

Answer 1

To solve the system of equations

1. \(3x - 4y = 40\)
2. \(5x - 5y = 55\)

we can follow these steps:

First, simplify the second equation: \[ 5x - 5y = 55 \implies x - y = 11 \implies x = y + 11 \]

Now, substitute \(x\) in the first equation: \[ 3(y + 11) - 4y = 40 \] \[ 3y + 33 - 4y = 40 \] \[ -y + 33 = 40 \] \[ -y = 40 - 33 \] \[ -y = 7 \implies y = -7 \]

Now substitute \(y\) back into the equation for \(x\): \[ x = y + 11 = -7 + 11 = 4 \]

Thus, the solution to the system of equations is: \[ (x, y) = (4, -7) \]

Therefore, the correct answer is: \((4, -7)\)