Question

Solve using elimination.

2x − 3y = 8
8x + y = 6

Answer 1

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

1) \( 2x - 3y = 8 \)
2) \( 8x + y = 6 \)

We want to eliminate one of the variables. Let's eliminate \(y\). To do this, we can manipulate the equations to have the same coefficient for \(y\).

From equation (2), let's multiply it by 3 to make the coefficient of \(y\) the same in both equations:

\[
3(8x + y) = 3(6)
\]

This gives us:

\[
24x + 3y = 18
\]

Now, we rewrite the system of equations:

1) \( 2x - 3y = 8 \)
2) \( 24x + 3y = 18 \)

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

\[
(2x - 3y) + (24x + 3y) = 8 + 18
\]

This simplifies to:

\[
26x = 26
\]

Now, divide both sides by 26:

\[
x = 1
\]

Now that we have \(x\), we can substitute it back into one of the original equations to find \(y\). We'll use equation (2):

\[
8x + y = 6
\]

Substituting \(x = 1\):

\[
8(1) + y = 6
\]

This simplifies to:

\[
8 + y = 6
\]

Now, solve for \(y\):

\[
y = 6 - 8
\]
\[
y = -2
\]

So the solution to the system of equations is:

\[
x = 1, \quad y = -2
\]

We can write the solution as an ordered pair:

\[
(1, -2)
\]