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=(2)/(3) \end{gathered}`

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

`\begin{gathered} y=(2)/(3) \\ \Rightarrow3x+(2)/(3)=4 \\ \Rightarrow3x=(10)/(3) \\ \Rightarrow x=(10)/(9) \end{gathered}`

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