# What is the error made in this strategy for solving linear equations?

The solution to the system $4y=3x+7$ and $9x+4y-139=0$ is shown below.

I solved for the solution and found that the answer is correct, and is $(11, 10)$. But, what is the mistake that is made here? I'm assuming the strategy is incorrect because it does not look like it would work with different situations involving systems.

• It's correct and that's how they are solved, there are quicker method though – Oussama Boussif Aug 12 '15 at 18:25
• So essentially she just simplified both equations, and then solved? – Madison Aug 12 '15 at 18:56
• Yes, she just subsituted and rearranged to get the solution that's how it's done – Oussama Boussif Aug 12 '15 at 18:58

As Oussama mentioned, there is an easier way to look at this. Write the first equation as: $$3x-4y=-7,$$ and the second equation as: $$9x+4y=139.$$ Then, we have: \begin{align} 9x+4y &= 139\\ 3x-4y &= -7. \end{align} Add the two equations together to get: \begin{align} 9x+4y &= 139\\ 3x-4y &= -7\\ \hline \\ 12x&= 132. \end{align} Notice that this method didn't require as many algebraic manipulations. Now, solve for $y$ just as before and you are done.