Advertisements
Advertisements
Question
Solve the following systems of equations:
4u + 3y = 8
`6u - 4y = -5`
Advertisements
Solution
Taking `1/x = u` then given equations become
4u + 3y = 8 ......(i)
6u - 4y = -5 ..........(ii)
From (i), we get
4u = 8 -3y
`=> u = (8 - 3y)/4`
Substituting u = `(8 - 3y)/4` in (ii) we get
From (ii), we get
`6((8-3y)/4) - 4y = -5`
`=> (3(8 - 3y))/4 - 4y = -5`
`=> (24 - 9y)/2 - 4y= -5`
`=> (24 - 9y - 8y)/2 = -5`
=> 24 - 17y = -10
=> -17y = -10 -24
=> -17y = -34
`=> y = (-34)/(-17) = 2`
Putting y = 2 in u =`(8-3y)/4` we get
`u = (8 - 3xx 2)/4 = (8-6)/4 = 2/4 = 1/2`
Hence x = 1/u = 2
So, the solution of the given system of equation is x 2, y
RELATED QUESTIONS
Solve the follownig system of equations by the method of cross-multiplication.
2x – 6y + 10 = 0
3x – 7y + 13 = 0
Solve the following system of equations by the method of cross-multiplication.
11x + 15y = – 23; 7x – 2y = 20
Solve the following system of equations by cross-multiplication method.
ax + by = a – b; bx – ay = a + b
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method
3x – 5y = 20
6x – 10y = 40
Solve the following system of equations by the method of cross-multiplication:
`(x + y)/(xy) = 2`
`(x - y)/(xy) = 6`
Solve each of the following systems of equations by the method of cross-multiplication :
`5/(x + y) - 2/(x - y) = -1`
`15/(x + y) + 7/(x - y) = 10`
where `x != 0 and y != 0`
Solve the following system of equations by the method of cross-multiplication:
5ax + 6by = 28
3ax + 4by = 18
Solve each of the following systems of equations by the method of cross-multiplication :
`x(a - b + (ab)/(a - b)) = y(a + b - (ab)/(a + b))`
`x + y = 2a^2`
Solve the following system of equations by the method of cross-multiplication:
bx + cy = a + b
`ax(1/(a - b) - 1/(a + b)) + cy(1/(b - a) - 1/(b + a)) = (2a)/(a + b)`
Solve the system of equations by using the method of cross multiplication:
`1/x + 1/y = 7, 2/x + 3/y = 17`
A father’s age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father.
Solve the following pair of equations:
x + y = 3.3, `0.6/(3x - 2y) = -1, 3x - 2y ≠ 0`
Solve the following pair of equations:
`x/a + y/b = a + b, x/a^2 + y/b^2 = 2, a, b ≠ 0`
Find the solution of the pair of equations `x/10 + y/5 - 1 = 0` and `x/8 + y/6 = 15`. Hence, find λ, if y = λx + 5.
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.
A person rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.
