Question Video: Determining the Point of Intersection of the Two Straight Lines Mathematics

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.