Question

In the xy-plane, the point (p,r) lies on the line with equation y=x+b, where b is a constant. The point with coordinates (2p,5r) lies on the line with equation y=2x+b. If p≠0, what is the value of
r and p?

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Answer 1

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According to your question:

y=x+b (given)

r=p+b (because p, r satisfy the equation)

r-p=b ———— 1

y=2x+b (given)

5r=4p+b (because 2p, 5r satisfy the equation)

5r-4p=b ———— 2

Equations 1 and 2 form pair of linear equations in two variables r and p. Solving equation 1 and 2 we get

r=-3b

p=-4b

Now,

r/p=-3b/-4b=3/4

Answer 2

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