Question

4x Solve the system of equations using elimination.
2x + y = 9
8x - 2y = 6


(9, 2)
』x

(5, 2)
一x

(2, 9)


(2, 5)


(5, -2)

Answer 1

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

1. \( 2x + y = 9 \) (Equation 1)
2. \( 8x - 2y = 6 \) (Equation 2)

First, we will manipulate the equations to eliminate one of the variables. Let's eliminate \(y\). To do that, we can multiply Equation 1 by 2, so that the coefficients of \(y\) in both equations will match:

\[
2(2x + y) = 2(9)
\]

This results in:

\[
4x + 2y = 18 \quad \text{(Equation 3)}
\]

Now we can rewrite our system:

1. \( 4x + 2y = 18 \) (Equation 3)
2. \( 8x - 2y = 6 \) (Equation 2)

Next, we will add Equation 3 and Equation 2 to eliminate \(y\):

\[
(4x + 2y) + (8x - 2y) = 18 + 6
\]

Simplifying, we get:

\[
4x + 8x + 2y - 2y = 24
\]

This simplifies to:

\[
12x = 24
\]

Now divide both sides by 12:

\[
x = 2
\]

Now that we have \(x\), we can substitute this value back into one of the original equations to find \(y\). Let's use Equation 1:

\[
2(2) + y = 9
\]

This simplifies to:

\[
4 + y = 9
\]

So,

\[
y = 9 - 4
\]
\[
y = 5
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (2, 5)
\]

So, the correct answer is:

**(2, 5)**