Question

Examine the system of equations.

−3x + y = 9,

2x + 4y = 8

Which variable is most efficient to isolate?
x in the first equation
y in the first equation
x in the second equation
y in the second equation

Answer 1

To determine which variable is most efficient to isolate, let’s look at the equations:

1. \(-3x + y = 9\)
2. \(2x + 4y = 8\)

**Isolating \(y\) in the first equation**:

From the first equation:
\[
y = 3x + 9
\]

**Isolating \(x\) in the second equation**:

From the second equation:
\[
2x + 4y = 8 \implies 2x = 8 - 4y \implies x = 4 - 2y
\]

Now let's compare the complexity of isolating these variables.

1. **In the first equation**:
- Isolating \(y\) gives a simple expression: \(y = 3x + 9\). This would allow you to substitute directly into the second equation.

2. **In the second equation**:
- Isolating \(x\) gives: \(x = 4 - 2y\). This is also a straightforward expression but involves \(y\).

Given both contexts, isolating \(y\) in the first equation results in a simple expression while having to substitute into the second equation.

Therefore, isolating **\(y\) in the first equation** is the most efficient choice as it allows for simpler substitution into the other equation.