Advertisements
Advertisements
प्रश्न
Solve for x and y:
71x + 37y = 253, 37x + 71y = 287
उत्तर
The given equations are:
71x + 37y = 253 …..(i)
37x + 71y = 287 ……(ii)
On adding (i) and (ii), we get:
108x + 108y = 540
⇒108(x + y) = 540
⇒(x + y) = 5 ……(iii)
On subtracting (ii) from (i), we get:
34x – 34y = -34
⇒34(x – y) = -34
⇒(x – y) = -1 ……(iv)
On adding (iii) from (i), we get:
2x = 5 – 1 = 4
⇒x = 2
On subtracting (iv) from (iii), we get:
2y = 5 + 1 = 6
⇒y = 3
Hence, the required solution is x = 2 and y = 3.
APPEARS IN
संबंधित प्रश्न
Find the value of k for which each of the following systems of equations has infinitely many solutions :
2x + 3y − 5 = 0
6x + ky − 15 = 0
Find the value of k for which each of the following systems of equations has infinitely many solutions :
4x + 5y = 3
kx + 15y = 9
Find the value of k for which each of the following system of equations have no solution
kx - 5y = 2
6x + 2y = 7
Find the values of a and b for which the following system of equations has infinitely many solutions:
(a - 1)x + 3y = 2
6x + (1 + 2b)y = 6
Find the value of k for which the system of equations has a unique solution:
2x + 3y = 5,
kx - 6y = 8
Find the value of k for which the system of linear equations has an infinite number of solutions:
2x + (k – 2)y = k,
6x + (2k - 1)y = (2k + 5).
A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. 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 equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 is inconsistent.
