Solve the system of equations.

Question

3x−4y=40

5x−5y=55
(1 point)
Responses

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

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

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

(8,−3)

Answer 1

To solve the system of equations:

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

We can simplify Equation 2 first:

Dividing the entire equation by 5 gives us: \[ x - y = 11 \quad \text{(Equation 3)} \]

Now, we can express \(y\) in terms of \(x\) using Equation 3: \[ y = x - 11 \]

Next, we can substitute this expression for \(y\) into Equation 1:

\[ 3x - 4(x - 11) = 40 \]

Distributing the -4: \[ 3x - 4x + 44 = 40 \]

Combining like terms: \[ -x + 44 = 40 \]

Now, isolate \(x\): \[ -x = 40 - 44 \] \[ -x = -4 \] \[ x = 4 \]

Now that we have \(x\), we can find \(y\) by substituting \(x = 4\) back into Equation 3: \[ y = 4 - 11 = -7 \]

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

So the correct answer is: (4, -7).