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

Determine the point of intersection of the two straight lines represented by the equations π‘₯ + 3𝑦 βˆ’ 2 = 0 and βˆ’π‘¦ + 1 = 0

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Video Transcript

Determine the point of intersection of the two straight lines represented by the equations π‘₯ 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 π‘₯- and 𝑦-values will be the same. As we have two equations with the two unknowns of π‘₯ 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 π‘₯-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 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 𝑦-value is one, which means that we can give our answer as the coordinate negative one, one.

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