Advertisements
Advertisements
Question
Solve the following systems of equations:
`2x - 3/y = 9`
`3x + 7/y = 2, y != 0`
Advertisements
Solution
The given systems of equation is
`2x - 3/y = 9` .....(i)
`3x + 7/y = 2, y != 0 ` ...(ii)
Taking `1/y = u` the given equations becomes
2x - 3u = 9 ....(iii)
3x + 7u = 2 ....(iv)
From (iii), we get
2x = 9 + 3u
`=> x = (9 + 3u)/2`
Substituting `x = (9 + 3u)/2` in iv we get
`3((9 + 3u)/2) + 7u = 2`
`=> (27 + 9u + 14u)/2 = 2`
`=> 27 + 23u = 2xx2`
`=> 23u = 4 - 27`
`=> u = (-23)/23 = -1`
hence `y = 1/u = 1/(-1) = -1`
Putting u = -1 in `x = (9 + 3u)/2` we get
`x = (9 + 3(-1))/2 = (9-3)/2 = 6/2 = 3`
=> x = 3
Hence, solution of the given system of equation is x = 3, y = -1
RELATED QUESTIONS
A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solve the following system of equations by the method of cross-multiplication. `\frac{a}{x}-\frac{b}{y}=0;\text{}\frac{ab^{2}}{x}+\frac{a^{2}b}{y}=a^{2}+b^{2};` Where x ≠ 0, y ≠ 0
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
2x + y = 5
3x + 2y = 8
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Solve the following systems of equations:
4u + 3y = 8
`6u - 4y = -5`
Solve the following systems of equations:
`1/(2x) + 1/(3y) = 2`
`1/(3x) + 1/(2y) = 13/6`
Solve the following system of equations:
`4/x + 3y = 14`
`3/x - 4y = 23`
Solve each of the following systems of equations by the method of cross-multiplication :
x + 2y + 1 = 0
2x − 3y − 12 = 0
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
`x/a + y/b = 2`
`ax - by = a^2 - b^2`
Solve each of the following systems of equations by the method of cross-multiplication :
`2/x + 3/y = 13`
`5/4 - 4/y = -2`
where `x != 0 and y != 0`
Solve the system of equations by using the method of cross multiplication:
3x – 2y + 3 = 0, 4x + 3y – 47 = 0
Solve the system of equations by using the method of cross multiplication:
6x – 5y – 16 = 0, 7x – 13y + 10 = 0
Solve the system of equations by using the method of cross multiplication:
2x + 5y – 1 = 0, 2x + 3y – 3 = 0
Solve the system of equations by using the method of cross multiplication:
`(ax)/b - (by)/a - (a + b) = 0, ax - by - 2ab = 0`
Complete the activity to find the value of x.
3x + 2y = 11 ...(i) and 2x + 3y = 4 ...(ii)
Solution:
Multiply equation (i) by ______ and equation (ii) by ______.
`square` × (3x + 2y = 11) ∴ 9x + 6y = 33 ...(iii)
`square` × (2x + 3y = 4) ∴ 4x + 6y = 8 ...(iv)
Subtract (iv) from (iii),
`square` x = 25
∴ x = `square`
Find the values of x and y in the following rectangle [see figure].
Solve the following pair of equations:
43x + 67y = – 24, 67x + 43y = 24
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.
Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re 1 per banana, and got a total of Rs 400. If he had sold the first lot at the rate of Re 1 per banana, and the second lot at the rate of Rs 4 for 5 bananas, his total collection would have been Rs 460. Find the total number of bananas he had.
