Question

What is the solution to the system of linear equations?
2x+4y=20
3x+2y=26​

Answer 1

We have

$

\begin{cases}

2x+4y=20\Longrightarrow x+2y=10\\

3x+2y=26\\

\end{cases}

$

Then multiply the second equation by -1 to get

$

\begin{cases}

x+2y=10\\

-3x-2y=-26\\

\end{cases}

$

Now add the equations that way you eliminate y-terms. You find that

$-2x=-16\Longrightarrow x=8$

Now plug in the x to either of the original equations and solve for y.

$

x+2y=10\\

8+2y=10\\

2y=2\Longrightarrow y=1

$

The solution is the intersection of two lines at $P(8,1)$.

Hope this helps.