### Video Transcript

Find the solution set of the two equations represented by ๐ฟ one and ๐ฟ two.

So ๐ฟ one and ๐ฟ two are lines. And when finding a solution, finding a solution from a graph is actually very straightforward. Itโs something where the lines intersect. And they intersect at this point and that point is two, three. Therefore, two, three would be our solution set.

Now, to be safe, we could solve for the solution another way. If we could find the equation of ๐ฟ one and the equation of ๐ฟ two, we could use the equations to solve for ๐ฅ and ๐ฆ. The equation of a line is ๐ฆ equals ๐๐ฅ plus ๐, where ๐ is the slope โ the rise over the run โ to the change in ๐ฆ divided by the change in ๐ฅ and ๐ is the ๐ฆ-intercept, where we cross the ๐ฆ-axis.

So letโs find the equation of ๐ฟ one. Letโs first solve for ๐. Where does it cross the ๐ฆ-axis? It crosses it here at ๐ฆ equals zero. And now for the slope, the rise over the run, so how much do we rise? We rise three spaces and we run two spaces. So we get ๐ฆ equals three halves ๐ฅ plus zero. So we donโt have to put the zero. We can just have ๐ฆ equals three-halves ๐ฅ.

Now, for the other line โ ๐ฟ two โ again letโs begin with ๐. We cross the ๐ฆ-axis at ๐ฆ equals three. And now, how much do we rise? We rise nothing. We rise zero. And then to reach our destination of the other point, we ran two. But it really doesnโt matter how much we run because zero divided by anything is simply zero and zero times ๐ฅ is zero and zero plus three is three. So the equation of that line is ๐ฆ equals three.

So right there, we know that ๐ฆ is equal to three, which we can see in our final answer. So if we wanted to solve for ๐ฅ, we could take three and plug it into the equation for ๐ฟ one and then solve for ๐ฅ. And we should get two.

So to solve for ๐ฅ, letโs go head and multiply both sides of the equation by two. And two times three is six. So we have six equals three ๐ฅ. So now, we divide both sides of the equation by three and find that two is equal to ๐ฅ, just as we found before.

So once again, the solution set of the two equations represented by ๐ฟ one and ๐ฟ two is two, three.