Question

Solving with Elimination Quick Check
4 of 54 of 5 Items






Question
Solve the system of equations.
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

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

(18, 7)

Answer 1

To solve the system of equations using elimination, we have:

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

First, we can simplify Equation 2:

\[
5x - 5y = 55 \implies x - y = 11 \implies y = x - 11 \tag{Equation 2 simplified}
\]

Next, we can substitute \( y = x - 11 \) into Equation 1:

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

Now, distribute the \(-4\):

\[
3x - 4x + 44 = 40
\]

Combine like terms:

\[
-x + 44 = 40
\]

Next, isolate \(x\):

\[
-x = 40 - 44 \implies -x = -4 \implies x = 4
\]

Now that we have \( x \), substitute it back into the simplified Equation 2 to find \( y \):

\[
y = 4 - 11 = -7
\]

Thus, the solution to the system of equations is:

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

The correct answer is \( \boxed{(4, -7)} \).