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
$\frac{r}{p}$
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Answer 1

Answer

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

According to your question:

According to your question:y=x+b (given)

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)5r-4p=b ———— 2

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)5r-4p=b ———— 2Equations 1 and 2 form pair of linear equations in two variables r and p. Solving equation 1 and 2 we get

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)5r-4p=b ———— 2Equations 1 and 2 form pair of linear equations in two variables r and p. Solving equation 1 and 2 we getr=-3b

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)5r-4p=b ———— 2Equations 1 and 2 form pair of linear equations in two variables r and p. Solving equation 1 and 2 we getr=-3bp=-4b

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)5r-4p=b ———— 2Equations 1 and 2 form pair of linear equations in two variables r and p. Solving equation 1 and 2 we getr=-3bp=-4bNow,

According to your question:y=x+b (given)r=p+b (because p, r satisfy the equation)r-p=b ———— 1y=2x+b (given)5r=4p+b (because 2p, 5r satisfy the equation)5r-4p=b ———— 2Equations 1 and 2 form pair of linear equations in two variables r and p. Solving equation 1 and 2 we getr=-3bp=-4bNow,r/p=-3b/-4b=3/4

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Answer 2

Answer:

• Point (p , r) lies on (y = x + b)
• Point (2p , 5r) lies on (y = 2x + b)
• Find the value of r/p

From the first statement

Since (p , r) lies on the line with equation (y = x + b), it will satisfy the equation :

⇢ r = p + b⠀⠀⠀— eq. ( I )

From the second statement

Point (2p , 5r) lies on the line with equation (y = 2x + b), it will satisfy the equation :

⇢ 5r = 2(2p) + b

⇢ 5r = 4p + b⠀⠀⠀— eq. ( II )

⠀⠀⠀⠀⠀───────────────

• Subtracting eq. ( I) from eq. ( II) :

⇒ 5r = 4p + b

⇒⠀r = p + b

⠀ –⠀ –⠀ –

______________

⇒ 4r = 3p

⇒ r/p = 3/4

∴ Hence, the required value of r/p is ¾.