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 π₯ + 3π¦ β 2 = 0 and β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 π¦ minus two equals zero and negative π¦ plus one equals zero.

Letβs say to answer this question weβre not going to draw these lines to get a graphical solution. Instead, weβre going to solve these algebraically. At the point of intersection, thatβs 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 weβre going to need to solve this simultaneously or by using a substitution method. However, in our second equation, we donβt 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 weβve 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.