Examine the system of equations.

Question

−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.