q8 a man has only 20 paqise coins and 25 paise coins in his purse If he has - Maths - Pair of Linear Equations in Two Variables

Question

q8 a man has only 20 paqise coins and 25 paise coins in his
purse If he has 50 coins in all totalling rs 11 25,howmany coins of
each type does he have?
q9 find the value of a and b for which the following system of
equations has infinitely many solutions
(2a-1)x-3y=5
3x=(b-2)y=3
q12 a motor boat takes 6 hours to cover 100km downstream and
80km upstream if the boat goes 75km downstream and returns back to
the starting point in 8 hours Find the speed of the boat in still
water and the speed of the stream

Ankush Jain · Accepted Answer

1) Here is the link for answer to your query!

https://www.meritnation.com/ask-answer/question/1-half-the-perimeter-of-a-rectangular-garden-whose-length-i/pair-of-linear-equations-in-two-variables/2430335

2)

If the given equations are as follows:

(2a-1)x-3y=5

3x-(b-2)y=3

For the given set of equations to have infinitely many solutions, we have

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ ... (1)

The given equations can be rewritten as:

(2a-1)x - 3y - 5 = 0

3x - (b-2) y - 3 = 0

Using (1), we get

$\frac{2 a - 1}{3} = \frac{- 3}{- (b - 2)} = \frac{- 5}{- 3}$

⇒ $\frac{2 a - 1}{3} = \frac{3}{b - 2} = \frac{5}{3}$

⇒ $\frac{2 a - 1}{3} = \frac{5}{3}$

⇒ a = 3 ... (2)

Similarly, $\frac{3}{b - 2} = \frac{5}{3}$

⇒ $9 = 5 b - 10$ [Using (2)]

⇒ 5b = 19

⇒ b = $\frac{19}{5}$

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