Question

Solve the following system of equations using the elimination method.

2x−3y=14
2
𝑥
−
3
𝑦
=
14
, 4x+3y=10
4
𝑥
+
3
𝑦
=
10

(1 point)
(,)

Answer 1

To solve the system of equations using the elimination method, we start with the two equations:

1. \( 2x - 3y = 14 \) (Equation 1)
2. \( 4x + 3y = 10 \) (Equation 2)

### Step 1: Align the equations

\[
\begin{align*}
(1) & \quad 2x - 3y = 14 \\
(2) & \quad 4x + 3y = 10 \\
\end{align*}
\]

### Step 2: Eliminate \(y\)

To eliminate \(y\), we can add the two equations directly, but first, we need to make the coefficients of \(y\) equal. In this case, we can multiply Equation 1 by 1 (keeping it the same) and Equation 2 by 1 (also keeping it the same) since \(3y\) in Equation 2 and \(-3y\) in Equation 1 are already opposites.

Now, we add the two equations:

\[
(2x - 3y) + (4x + 3y) = 14 + 10
\]

This simplifies to:

\[
2x + 4x - 3y + 3y = 24
\]

Which results in:

\[
6x = 24
\]

### Step 3: Solve for \(x\)

Now we can divide both sides by 6:

\[
x = \frac{24}{6} = 4
\]

### Step 4: Substitute \(x\) back into one of the original equations

Now that we have \(x = 4\), we can substitute it back into either original equation to find \(y\). Let's use Equation 1:

\[
2(4) - 3y = 14
\]

This simplifies to:

\[
8 - 3y = 14
\]

### Step 5: Solve for \(y\)

Subtract 8 from both sides:

\[
-3y = 14 - 8
\]
\[
-3y = 6
\]

Now divide both sides by -3:

\[
y = \frac{6}{-3} = -2
\]

### Conclusion

The solution to the system of equations is:

\[
(x, y) = (4, -2)
\]

Thus, the final answer is:

\[
\boxed{(4, -2)}
\]