24. Which method is BEST for solving the system of linear equations shown? $$ \begin{array}{l}2 x+6 y=12 \ 3 x-6 y=3\end{array} $$ substitution elimination graphing

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To determine the best method for solving the system of linear equations:

$$
\begin{aligned}
2x + 6y &= 12 \
3x - 6y &= 3
\end{aligned}
$$

**Elimination** is the most efficient method for this system. Here's why:

1. **Elimination Method**:
   - **Step 1**: Add the two equations together to eliminate $$ y $$:
     $$
     (2x + 6y) + (3x - 6y) = 12 + 3 \
     5x = 15 \
     x = 3
     $$
   - **Step 2**: Substitute $$ x = 3 $$ back into one of the original equations to find $$ y $$:
     $$
     2(3) + 6y = 12 \
     6 + 6y = 12 \
     6y = 6 \
     y = 1
     $$
   - **Solution**: $$ x = 3 $$, $$ y = 1 $$

2. **Why Not Substitution?**
   - Substitution would require solving one of the equations for one variable first, which involves fractions and is more time-consuming for this particular system.

3. **Why Not Graphing?**
   - Graphing is less precise and more time-consuming, especially since the system can be easily solved algebraically.

**Answer:** Elimination
The best method to solve the system is elimination.

24. Which method is BEST for solving the system of linear equations shown? \[ \begin{array}{l}2 x+6 y=12 \\ 3 x-6 y=3\end{array} \] substitution elimination graphing

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