Video: Finding the Point of Intersection of Two Straight Lines

Find the point of intersection of the two straight lines βˆ’11π‘₯ + 20 = 0 and βˆ’11𝑦 + 2 = 0.

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Video Transcript

Find the point of intersection of the two straight lines negative 11π‘₯ plus 20 equals zero and negative 11𝑦 plus two equals zero.

We could solve this problem algebraically or graphically. Let’s begin by considering the two equations given. In both equations, we only have one unknown or variable. In the first equation, negative 11π‘₯ plus 20 equals zero, the only variable is π‘₯. Therefore, we can solve this equation to calculate a value of π‘₯. We begin by adding 11π‘₯ to both sides such that 20 is equal to 11π‘₯. We can then divide both sides of this equation by 11 such that π‘₯ is equal to 20 over 11.

We can then repeat this process for the second equation negative 11𝑦 plus two equals zero. Firstly, adding 11𝑦 to both sides gives us two is equal to 11𝑦. Dividing through by 11 gives us 𝑦 is equal to two elevenths or two over 11. The values that satisfy our two equations are therefore π‘₯ equals twenty elevenths and 𝑦 equals two elevenths. This tells us that the point of intersection of the two straight lines has coordinates twenty elevenths, two elevenths.

We can check this answer by sketching our two equations in the π‘₯𝑦-plane. Any equation in the form π‘₯ equals π‘Ž, where π‘Ž is some constant, will correspond to a vertical line. The line will cross the axis at π‘₯ equals π‘Ž. Therefore, the equation π‘₯ equals twenty elevenths is a vertical line crossing the π‘₯-axis at twenty elevenths. In the same way, any equation in the form 𝑦 equals π‘Ž, where π‘Ž is some constant, will be a horizontal line. The equation 𝑦 equals two elevenths is a horizontal line that crosses the 𝑦-axis at two elevenths. The diagram confirms that the point of intersection of the two straight lines negative 11π‘₯ plus 20 equals zero and negative 11𝑦 plus two equals zero is twenty elevenths, two elevenths.

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