Question

How to Use Elimination to Solve a System of Two Linear Equations
1. Identify
Answer
as the best method for the problem.
2. Find a
i Answer
with equal or opposite coefficients in the system.
3. Add or subtract one Answer, from the other.
4. | Answer
1-111！、
the one-variable equation.
5. Substitute the value of that variable into the other
--;
Answer
6. Solve for the second
-=,
i Answer
7. Check your answer. Use
Answer
and/or graphing.
substitution
:: Solve
:: equation
elimination
:: variable
 equation
¿variable

Answer 1

Here's how to use elimination to solve a system of two linear equations step-by-step, filling in the answers for the placeholders indicated:

1. **Identify** **elimination** as the best method for the problem.

2. Find a **pair of equations** with equal or opposite coefficients in the system. This may involve multiplying one or both of the equations by a suitable number to achieve this.

3. Add or subtract one **equation** from the other to eliminate one variable.

4. **Solve** the one-variable equation. This means you'll be left with an equation that contains just one variable, which you can solve for that variable.

5. Substitute the value of that variable into the other **equation** to find the other variable.

6. Solve for the second **variable**. This will give you the value of the second variable in the system of equations.

7. Check your answer. Use **substitution** and/or graphing to ensure the solution satisfies both original equations.

### Example:

Let's use elimination with a specific example to clarify the steps:

Given the system of equations:
1. \( 2x + 3y = 6 \)
2. \( 4x - 3y = 10 \)

#### Step 1
Identify **elimination** as the best method for the problem.

#### Step 2
We have equal and opposite coefficients for \(y\) (3 and -3).

#### Step 3
Add both equations:
\[
(2x + 3y) + (4x - 3y) = 6 + 10
\]
This simplifies to:
\[
6x = 16
\]

#### Step 4
**Solve** the one-variable equation:
\[
x = \frac{16}{6} = \frac{8}{3}
\]

#### Step 5
Substitute \(x = \frac{8}{3}\) back into one of the original equations. We'll use the first equation:
\[
2\left(\frac{8}{3}\right) + 3y = 6
\]

#### Step 6
Solve for \(y\):
\[
\frac{16}{3} + 3y = 6
\]
Subtract \(\frac{16}{3}\) from both sides:
\[
3y = 6 - \frac{16}{3}
\]
Convert 6 to a fraction:
\[
3y = \frac{18}{3} - \frac{16}{3} = \frac{2}{3}
\]
Thus,
\[
y = \frac{2}{9}
\]

#### Step 7
Check your answer. Substitute \(x = \frac{8}{3}\) and \(y = \frac{2}{9}\) back into both original equations to verify they hold true.

Following these steps will effectively use elimination to solve a system of linear equations successfully.