To determine the most efficient variable to solve for, we should analyze the equations.
The two equations are:
- \( x + 3y = 7 \) (Equation 1)
- \( 2x + 4y = 9 \) (Equation 2)
Let's look at the first equation:
From Equation 1, we can solve for \( x \):
\[ x = 7 - 3y \]
This expresses \( x \) in terms of \( y \), allowing us to substitute \( x \) into the second equation if needed.
Now, let's check what happens if we try to solve for \( y \) in the first equation:
\[ 3y = 7 - x \implies y = \frac{7 - x}{3} \]
We can also solve \( y \) from the second equation:
From Equation 2, we can simplify it by dividing everything by 2:
\[ x + 2y = 4.5 \quad \Rightarrow \quad 2y = 4.5 - x \quad \Rightarrow \quad y = \frac{4.5 - x}{2} \]
Now we realize that both equations can be cumbersome, but attempting to solve for either variable in the first equation seems relatively straightforward.
However, if we analyze the second equation \( 2x + 4y = 9 \), it actually suggests a dependency with the first equation, indicating potential redundancy.
Now given that, if we focus on finding the simplest way to isolate one variable immediately:
Conclusion:
Since the first equation \( x + 3y = 7 \) can be readily manipulated, it is more efficient to solve for \( x \) in the first equation.
This means the best choice would be:
x in the first equation.
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