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Question 2.2: Points of Intersection Find the points of intersection of t......

Points of Intersection

Find the points of intersection of the graphs of the equations x² – y = 3 and x – y = 1.

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Solve for y in each equation and then set them equal to each other:

 

y=x2−3,y=x−1  implies  x2−3=x−1 .y=x^{2}-3,y=x-1{ \ \mathrm{~implies~}} \ x^{2}-3=x-1\,.

 

Solving this equation, you obtain x² – x – 2 = (x – 2)(x + 1) = O. Hence x = 2 and x = -1, so the points of intersection are (2,1) and (-1,-2).

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