Advertisements
Advertisements
Question
Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv
Solution
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
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[5y]/2 - x/3 = 8`
`y/2 + [5x]/3 = 12`
10% of x + 20% of y = 24
3x - y = 20
Solve the following simultaneous equations:
65x - 33y = 97
33x - 65y = 1
Solve the following pairs of equations:
y - x = 0.8
`(13)/(2(x + y)) = 1`
Solve the following pairs of equations:
`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`
`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2
`4x + 6/y = 15 and 6x - 8/y = 14.` Hence, find a if y = ax - 2.
If the following three equations hold simultaneously for x and y, find the value of 'm'.
2x + 3y + 6 = 0
4x - 3y - 8 = 0
x + my - 1 = 0
The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.
The present ages of Kapil and Karuna are in the ratio 2 : 3. Six years later, the ratio will be 5 : 7. Find their present ages.
In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.
