Question

Solve the system using Elimination.


2x - 5y = 6
3x + y = 26


(1 point)
Responses

(4,-2)
(4,-2)

(8,2)
(8,2)

(5,3)

Answer 1

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

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

First, we can eliminate \( y \) by manipulating the second equation so that the coefficient of \( y \) matches that of the first equation. We can multiply equation (2) by 5:

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

Now we have the following modified equations:

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

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

\[
(2x - 5y) + (15x + 5y) = 6 + 130
\]
\[
2x + 15x = 136
\]
\[
17x = 136
\]

Now, we divide both sides by 17:

\[
x = 8
\]

Next, we plug \( x = 8 \) back into one of the original equations to find \( y \). We'll use the second equation \( 3x + y = 26 \):

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

Now we'll solve for \( y \):

\[
y = 26 - 24
\]
\[
y = 2
\]

So, the solution to the system of equations is:

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

Thus, the correct answer is:

**(8,2)**