Question

Using the given system of equations, what variable will you eliminate and why?3x + y = 43x + 4y = 6

Answer 1

Given the system of equations,

$\begin{cases}3x+y=4 \\ 3x+4y=6\end{cases}$

To use the elimination method, the better option is to eliminate the x variable, since the coefficient that accompanies x in both equations is the same. Then, subtracting the first equation from the second one,

$\begin{gathered} (3x+4y)-(3x+y)=6-4 \\ \Rightarrow4y-y=2 \\ \Rightarrow3y=2 \\ \Rightarrow y=\frac{2}{3} \end{gathered}$

Then, we can use the value of y to find x, as shown below

$\begin{gathered} y=\frac{2}{3} \\ \Rightarrow3x+\frac{2}{3}=4 \\ \Rightarrow3x=\frac{10}{3} \\ \Rightarrow x=\frac{10}{9} \end{gathered}$

The better option is to eliminate x first because its coefficient is the same (3) in both equations.