Advertisements
Advertisements
प्रश्न
Solve the following systems of equations:
`2/x + 5/y = 1`
`60/x + 40/y = 19, x = ! 0, y != 0`
उत्तर
Taking 1/x = u and 1/y = v the given become
2u + 5v = 1 ......(1)
60u + 40u = 19 .....(ii)
Let us eliminate ‘u’ from equation (i) and (ii), multiplying equation (i) by 60 and equation (ii) by 2, we get
120u + 300v = 60 ....(iii)
120u + 80v = 38 ....(iv)
Subtracting (iv) from (iii), we get
300v - 80v = 60 - 38
=> 220v = 22
=> `v = 22/220 = 1/10`
Putting `v = 1/10` in equation (i) we get
`2u + 5 xx 1/10 = 1`
`=> 2u + 1/2 = 1`
`=> 2u = 1 - 1/2`
`=> 2u = (2-1)/2 = 1/2`
`=> 2u = 1/2`
`=> u = 1/4`
hence `x = 1/u = 4` and `y = 1/v = 10`
So, the solution of the given system of equation is x = 4, y = 10
APPEARS IN
संबंधित प्रश्न
Solve the following pair of linear equations by the substitution method.
x + y = 14
x – y = 4
Form the pair of linear equations for the following problems and find their solution by substitution method.
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
Solve the following systems of equations:
`2/x + 3/y = 9/(xy)`
`4/x + 9/y = 21/(xy), where x != 0, y != 0`
Solve the following systems of equations:
`5/(x + 1) - 2/(y -1) = 1/2`
`10/(x + 1) + 2/(y - 1) = 5/2` where `x != -1 and y != 1`
Solve the following systems of equations:
`2(1/x) + 3(1/y) = 13`
`5(1/x) - 4(1/y) = -2`
5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of
1 pen and 1 pencil.
The solution of the equation 2x – y = 2 is ______
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively ______.
Two numbers are in the ratio 5 : 6. If 8 is subtracted from the numbers, the ratio becomes 4 : 5. Find the numbers.
There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.
