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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.
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.
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