algebra precalculus - 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.