Advertisements
Advertisements
Question
Solve the following simultaneous equations :
3(2u + v) = 7uv
3(u + 3v) = 11uv
Advertisements
Solution
3(2u + v) = 7uv
3(u + 3v) = 11uv
Dividing by uv, we get,
`(6)/v + (3)/u` = 7 ........(1)
3(u + 3v) = 11uv
3u + 9v = 11uv
Dividing by uv, we get
`(3)/v + (8)/u` = 11...........(2)
Multiplying (1) by 3, we get,
`(18)/v + (9)/u` = 21........(3)
Subtracting (2) from (3), we get,
`(15)/v` = 10
⇒ v = `(15)/(10) = (3)/(2)`
∴ `(3)/u`
= `7 - 6 xx (2)/(3)`
= 7 - 4
= 3
⇒ u = 1
Thus, the solution set is `(1,3/2)`.
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`1/5( x - 2 ) = 1/4( 1 - y )`
26x + 3y + 4 = 0
For solving pair of equation, in this exercise use the method of elimination by equating coefficients:
y = 2x - 6; y = 0
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74
Solve the following pairs of equations:
`(xy)/(x + y) = (6)/(5)`
`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0
Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.
The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?
9 pens and 5 pencils cost Rs.32, and 7 pens and 8 pencils cost Rs.29. Find the unit price for each pen and pencil.
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.
