Question

Solve the system using Elimination.
2x−5y=6

3x+y=26
(1 point)
Responses

(5,3)
(5,3)

(8,2)
(8,2)

(5,3)
(5,3)

(4,-2)

Answer 1

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

1) \( 2x - 5y = 6 \)
2) \( 3x + y = 26 \)

First, we can manipulate the second equation to eliminate \(y\). To do this, we can multiply the second equation by \(5\) so that both equations will have \(y\) terms with the same coefficients:

\[
5(3x + y) = 5(26)
\]
\[
15x + 5y = 130
\]

Now we have the following system:

1) \( 2x - 5y = 6 \)
2) \( 15x + 5y = 130 \)

Next, we add the two equations together to eliminate \(y\):

\[
(2x - 5y) + (15x + 5y) = 6 + 130
\]
This simplifies to:

\[
17x = 136
\]

Now, solve for \(x\):

\[
x = \frac{136}{17} = 8
\]

Now that we have \(x\), we can substitute it back into one of the original equations to find \(y\). We'll use the second equation \(3x + y = 26\):

\[
3(8) + y = 26
\]
\[
24 + y = 26
\]
\[
y = 26 - 24 = 2
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (8, 2)
\]

The correct response is:

(8, 2)