Question

Solving Simultaneous Equations Using Elimination Practice
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Question
Solve the following system of equations using the elimination method.

2x−3y=14
, 4x+3y=10


(1 point)
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,
)
Remaining Attempts : 3
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Answer 1

To solve the system of equations using the elimination method, we need to eliminate one of the variables. Here are the two equations we have:

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

**Step 1: Align the equations.**

We can add Equation 1 and Equation 2 directly since the coefficient of \( y \) in Equation 1 is \( -3 \) and in Equation 2 is \( +3 \). This means that if we add the equations, the \( y \) terms will cancel out.

**Step 2: Add the equations.**

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

This simplifies to:

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

\[
6x = 24
\]

**Step 3: Solve for \( x \).**

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

**Step 4: Substitute \( x \) back into one of the original equations to solve for \( y \).**

We can use Equation 1:

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

This simplifies to:

\[
8 - 3y = 14
\]

Subtract 8 from both sides:

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

Now, divide by -3:

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

**Final Answer:**

The solution to the system of equations is:

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