Video Transcript
Determine the point of intersection
of the two straight lines represented by the equations 𝑥 plus three 𝑦 minus two
equals zero and negative 𝑦 plus one equals zero.
Let’s say that to answer this
question, we’re not going to draw these lines to get a graphical solution. But instead, we’re going to solve
these algebraically. At the point of intersection,
that’s the place where the two lines meet or cross, the 𝑥- and 𝑦-values must be
the same. As we have two equations with the
two unknowns of 𝑥 and 𝑦, then we can solve simultaneously or by using a
substitution method. However, in our second equation,
notice that we don’t actually have an 𝑥-value. So perhaps the more efficient way
to solve for 𝑥 and 𝑦 is by using a substitution method. If we take this second equation of
negative 𝑦 plus one equals zero and rearrange this to make 𝑦 the subject, by
adding 𝑦 to both sides, we would get one equals 𝑦 or 𝑦 equals one.
And now that we have established
that 𝑦 is equal to one, we can substitute this into the first equation. This gives us 𝑥 plus three times
one minus two equals zero. Evaluating this, we have 𝑥 plus
one equals zero. And so 𝑥 is equal to negative
one. Now we know that at the point of
intersection of these two lines, the 𝑥-value is negative one and the 𝑦-value is
one, which means that we can give our answer as the coordinates negative one,
one.
