Solve the system of equations.

Question

3x−4y=40

5x−5y=55
(1 point)
Responses

(4,−7)
left parenthesis 4 comma negative 7 right parenthesis

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

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

(18, 7)

Answer 1

To solve the system of equations:

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

First, we can simplify Equation 2:

\[ 5x - 5y = 55 \implies x - y = 11 \implies x = y + 11 \quad \text{(Equation 3)} \]

Now, we can substitute Equation 3 into Equation 1:

\[ 3(y + 11) - 4y = 40 \]

Distributing \(3\):

\[ 3y + 33 - 4y = 40 \]

Now combine like terms:

\[ -1y + 33 = 40 \]

Subtract 33 from both sides:

\[ -1y = 7 \implies y = -7 \]

Now we can substitute \(y\) back into Equation 3 to find \(x\):

\[ x = -7 + 11 = 4 \]

The solution to the system of equations is:

\[ (x, y) = (4, -7) \]

So the answer is \((4, -7)\).