Question

Given the system of equations below:
3x-2y=10
3x+2y=14


Part II: Solve the system of equations using the method you discussed in Part I. Show ALL work. Write your final answer as an ordered pair x,y
.

Answer 1

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

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

**Step 1: Eliminate one variable.**

To eliminate \( y \), we will add both equations together.

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

This simplifies to:

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

The \( -2y \) and \( +2y \) cancel each other out:

\[
6x = 24
\]

**Step 2: Solve for \( x \).**

Now, divide both sides by 6:

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

**Step 3: Substitute \( x \) back into one of the original equations to find \( y \).**

Let's use Equation 1 for this:

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

This gives:

\[
12 - 2y = 10
\]

Now, isolate \( -2y \):

\[
-2y = 10 - 12
\]

\[
-2y = -2
\]

Now, divide by -2:

\[
y = \frac{-2}{-2} = 1
\]

**Step 4: Write the final answer as an ordered pair.**

The solution to the system of equations is:

\[
(x, y) = (4, 1)
\]

Thus, the final answer is \((4, 1)\).