Advertisements
Advertisements
Question
Solve for x and y:
`3/x + 6/y = 7, 9/x + 3/y = 11`
Solution
The given equations can be written as
`3/x + 6/y = 7` …….(i)
`9/x + 3/y = 11` ……(ii)
Multiplying (i) by 3 and subtracting (ii) from it, we get
`18/y - 3/y = 21 – 11`
⇒ `15/y = 10`
⇒` y = 15/10 = 3/2`
Substituting y = `3/2` in (i), we have
`3/x + (6×2)/3 = 7`
`⇒ 3/x = 7 – 4 = 3`
Hence, x = 1 and y = `3/2`.
APPEARS IN
RELATED QUESTIONS
Find the value of k for which each of the following system of equations has infinitely many solutions :
2x +3y = k
(k - 1)x + (k + 2)y = 3k
Solve for x and y:
2x + 3y + 1 = 0
`(7-4x)/3 = y`
Solve for x and y:
`(bx)/a - (ay)/b + a + b = 0, bx – ay + 2ab = 0`
Solve for x and y:
`x + y = a + b, ax - by = a^2 - b^2`
Find two numbers such that the sum of twice the first and thrice the second is 92, and four times the first exceeds seven times the second by 2.
The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream
A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 litres of a 40% acid solution?
Find the value of k for which the system of linear equations has an infinite number of solutions.
2x + 3y=9,
6x + (k – 2)y =(3k – 2
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
2x + 3y = 7 and 2px + py = 28 – qy,
if the pair of equations have infinitely many solutions.
