### Video Transcript

Determine the point of intersection
of the two straight lines represented by the equations π₯ plus three π¦ minus two
equals zero and negative π¦ plus one equals zero.

Letβs say to answer this question
weβre not going to draw these lines to get a graphical solution. Instead, weβre going to solve these
algebraically. At the point of intersection,
thatβs the place where the two lines meet or cross, the π₯- and π¦-values will be
the same. As we have two equations with the
two unknowns of π₯ or π¦, then weβre going to need to solve this simultaneously or
by using a substitution method. However, in our second equation, we
donβt actually have an π₯-value. So perhaps, a substitution method
here is the easiest. If we take our second equation of
negative π¦ plus one equals zero and rearrange this to make π¦ the subject, then by
adding π¦ to both sides, we would get one equals π¦ or π¦ equals one.

Now that weβve established that π¦
is equal to one, we can plug this into the first equation. This gives us π₯ plus three times
one subtract two equals zero. Evaluating this, we have π₯ plus
one equals zero. Subtracting negative one, we have
π₯ is equal to negative one. Now we know that at the point of
intersection of these two equations, the π₯-value is negative one and the π¦-value
is one, which means that we can give our answer as the coordinate negative one,
one.