Solving Simultaneous Equations Using Elimination Practice

Question

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Question
Solve the following system of equations using the elimination method.

2x−3y=14
, 4x+3y=10


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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:

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