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

Determine the point of intersection of the two straight lines represented by the equations 𝑥 + 3𝑦 − 2 = 0 and −𝑦 + 1 = 0

01:36

### 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 to answer this question we’re not going to draw these lines to get a graphical solution. 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 will be the same. As we have two equations with the two unknowns of 𝑥 or 𝑦, then we’re going to need to solve this simultaneously or by using a substitution method. However, in our second equation, we don’t actually have an 𝑥-value. So perhaps, a substitution method here is the easiest. If we take our second equation of negative 𝑦 plus one equals zero and rearrange this to make 𝑦 the subject, then by adding 𝑦 to both sides, we would get one equals 𝑦 or 𝑦 equals one.

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