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 :
`[5y]/2 - x/3 = 8`
`y/2 + [5x]/3 = 12`
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 2x + y = 23 and 4x - y = 19; find the values of x - 3y and 5y - 2x.
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
Solve the following pairs of equations:
`(xy)/(x + y) = (6)/(5)`
`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0
`4x + 6/y = 15 and 6x - 8/y = 14.` Hence, find a if y = ax - 2.
Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. Find the number.
A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?
A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.
