Solve the system of equations.

Question

3x−4y=40

5x−5y=55
(1 point)
Responses

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

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

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

(14, 3)

Answer 1

To solve the system of equations:

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

Let's first simplify Equation 2 by dividing all terms by 5:

\[ x - y = 11 \] So we can rewrite it as: \[ x = y + 11 \quad (Equation 3) \]

Now we can substitute Equation 3 into Equation 1. Substitute \( x = y + 11 \) 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: \[ -1y = 7 \]

Multiplying both sides by -1: \[ y = -7 \]

Now substitute \( y = -7 \) back into Equation 3 to find \( x \):

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

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

Looking at the options provided, the correct answer is:

\((4, -7)\)