Question

page 16 of 16
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

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

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

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

(14, 3)

Answer 1

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

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

Let's start by rearranging the second equation to make it easier to work with. We can simplify the second equation by dividing everything by 5:

\[
x - y = 11
\]

Now we can rewrite the system:

1. \( 3x - 4y = 40 \)
2. \( x - y = 11 \)

Next, we'll isolate \( x \) from the second equation:

\[
x = y + 11
\]

Now substitute \( x \) in the first equation:

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

Expanding this:

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

Combining like terms:

\[
-y + 33 = 40
\]

Now isolate \( y \):

\[
-y = 40 - 33 \\
-y = 7 \\
y = -7
\]

Now that we have \( y \), we can find \( x \) using the second equation:

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

So, the solution to the system of equations is \( (4, -7) \).

Therefore, the correct response is:

**(4, -7)**