Advertisements
Advertisements
Question
The value of expression mx - ny is 3 when x = 5 and y = 6. And its value is 8 when x = 6 and y = 5. Find the values of m and n.
Advertisements
Solution
The value of expression mx - ny is 3 when x = 5 and y = 6.
⇒ 5m - 6n = 3 .....(1)
The value of expression mx - ny is 8 when x = 6 and y = 5.
⇒ 6m - 5n = 8 ....(2)
Multiply equation (1) by 6 and equation (2) by 5, We get:
30m - 36n = 18 ....(3)
30m - 25n = 40 .....(4)
Subtracting equation (4) from (3)
30m - 36n = 18
- 30m - 25n = 40
- + -
- 11n = - 22
n = 2
Substituting n = 2 in equation (1), we get
5m - 6(2) = 3
⇒ 5m = 15
⇒ m = 3
∴ Solution is m = 3 and n = 2.
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
2x − 3y − 3 = 0
`[2x]/3 + 4y + 1/2` = 0
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
Solve :
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5`
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x`
Solve the following simultaneous equations:
41x + 53y = 135
53x + 41y = 147
Solve the following pairs of equations:
`(2)/x + (3)/y = (9)/(xy)`
`(4)/x + (9)/y = (21)/(xy)`
Where x ≠ 0, y ≠ 0
The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.
In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.
Two mobiles S1 and S2 are sold for Rs. 10,490 making 4% profit on S1 and 6% on S2. If the two mobiles are sold for Rs.10,510, a profit of 6% is made on S1 and 4% on S2. Find the cost price of both the mobiles.
