Advertisements
Advertisements
Question
Solve the following systems of equations:
`2/x + 3/y = 9/(xy)`
`4/x + 9/y = 21/(xy), where x != 0, y != 0`
Solution
The system of given equation is
`2/x + 3/y = 9/(xy)` ....(i)
`4/x + 9/y = 21/(xy), x != 0, y != 0` ......(ii)
Multiplying equation (i) adding equation (ii) by ,xy we get
2y + 3x = 9 ....(iii)
4y + 9x = 21 .....(iv)
From (iii), we get
3x = 9 - 2y
`=> x = (9 - 2y)/3`
Substituting x `= (9 - 2y)/3` in equation (iv) weget
`4x + 9((9 - 2y)/3) = 21`
=> 4y + 3(9 - 2y) = 21
=> 4y + 27 - 6y = 21
`=> -2y = 21 - 27`
=> -2y = -6
`=> y = (-6)/(-2) = 3`
Putting y = 3 in x = (9 - 2y)/3 we get
`x = (9 - 2xx3)/3`
`= (9-6)/3`
= 3/3
= 1
Hence, solution of the system of equation is x = 1, y = 3
APPEARS IN
RELATED QUESTIONS
A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.
Solve the following pair of linear equations by the substitution method.
`(3x)/2 - (5y)/3 = -2`
`x/y+y/2 = 13/6`
Form the pair of linear equations for the following problem and find their solution by substitution method.
The difference between two numbers is 26 and one number is three times the other. Find them.
Solve the following systems of equations:
`22/(x + y) + 15/(x - y) = 5`
`55/(x + y) + 45/(x - y) = 14`
Solve the following systems of equations:
`x+y = 2xy`
`(x - y)/(xy) = 6` x != 0, y != 0
Solve the following simultaneous equations by Cramer's method.
`x+y=7,2x-3y=9`
Solve the following set of simultaneous equation.
2x + 3y + 4 = 0; x − 5y = 11
Find the solution of the pair of the equation :
`3/x + 8/y = - 1; 1/x - 2/y = 2`, x, y ≠ 0
For the equation 3x − 2𝑦 = 17, find the value of x when y = −1 and find the value of y when x = 3
3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹ 2,100. If the cost of 1 chair is ₹ x and the cost of 1 table is ₹ y, then the situation can be represented algebraically as ______.
