Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Solve for x and y:
2x - `(3y)/4 = 3 ,5x = 2y + 7`
рдЙрддреНрддрд░
The given equations are:
2x - 3ЁЭСж4 = 3 …..(i)
5x = 2y + 7 ……..(ii)
On multiplying (i) by 2 and (ii) by `3/4`, we get:
4x -`3/2y = 6` …...(iii)
`15/4 x = 3/2y + 21/4 ` ................(iv)
On subtracting (iii) and (iv), we get:
`1/4x =-3/4`
⇒ x = 3
On substituting x = 3 in (i), we get:
`2 xx 3 - (3y)/4 = 3 `
⇒ `(3y)/4 = (6-3) = 3`
⇒ y = `(3xx4)/4 = 4`
Hence, the solution is x = 3 and y = 4.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?
Find the value of k for which each of the following system of equations have no solution
kx - 5y = 2
6x + 2y = 7
Solve for x and y:
4x - 3y = 8, 6x - y = `29/3`
Solve for x and y:
6x + 5y = 7x + 3y + 1 = 2(x + 6y – 1)
Solve for x and y:
x + y = 5xy, 3x + 2y = 13xy
Solve for x and y:
`5/x + 2/y = 6, (−5)/x + 4/y = -3`
Show that the system equations
2x - 3y = 5,
6x - 9y = 15
has an infinite number of solutions
Places A and B are 160 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.
Find the value of k for which the system of linear equations has an infinite number of solutions.
10x + 5y – (k – 5) = 0,
20x + 10y – k = 0.
Read the following passage:
A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is тВ╣9,000 and from batch II is тВ╣26,000. Assume that each poor child pays тВ╣x per month and each rich child pays тВ╣y per month. |
Based on the above information, answer the following questions:
- Represent the information given above in terms of x and y.
- Find the monthly fee paid by a poor child.
OR
Find the difference in the monthly fee paid by a poor child and a rich child. - If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?