Advertisements
Advertisements
प्रश्न
Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv
Advertisements
उत्तर
8v - 3u = 5uv
6v - 5u = -2uv
Dividing both sides of each equation by uv, we get,
`(8)/u - (3)/v` = 5..........(1)
`(6)/u - (5)/v` = -2.........(2)
Multiplying (1) by 3 and (2) by 4, we get,
`(24)/u - (9)/v` = 15.......(3)
`(24)/u - (20)/v` = -8........(4)
Subtracting (4) from (3), we get,
`(11)/v` = 23
⇒ v = `(11)/(23)`
∴ `(6)/u - (5)/(11) xx 23` = -2
⇒ `(6)/u - (115)/(11)` = -2
⇒ `(6)/u`
= `-2 + (115)/(11)`
= `(-22 + 115)/(11)`
= `(93)/(11)`
⇒ u = `(6 xx 11)/(93)`
= `(22)/(31)`
Thus, the solution set is `(22/11 , 11/23)`.
APPEARS IN
संबंधित प्रश्न
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
13x+ 11y = 70
11x + 13y = 74
10% of x + 20% of y = 24
3x - y = 20
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following pairs of equations:
y - x = 0.8
`(13)/(2(x + y)) = 1`
Solve the following pairs of equations:
`(x + y)/(xy)` = 2
`(x - y)/(xy)` = 6
Solve the following pairs of equations:
`(2)/(x + 1) - (1)/(y - 1) = (1)/(2)`
`(1)/(x + 1) + (2)/(y - 1) = (5)/(2)`
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.
An eraser costs Rs. 1.50 less than a sharpener. Also, the cost of 4 erasers and 3 sharpeners is Rs.29. Taking x and y as the costs (in Rs.) of an eraser and a sharpener respectively, write two equations for the above statements and find the value of x and y.
A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.
Two mobiles S1 and S2 are sold for Rs. 10,490 making 4% profit on S1 and 6% on S2. If the two mobiles are sold for Rs.10,510, a profit of 6% is made on S1 and 4% on S2. Find the cost price of both the mobiles.
