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Answers
Answer:
Step-by-step explanation:
(1)1/x-1/y=1------------1
1/x+1/y=7-----------2
taking 1/x=p and 1/y=q
∴eq 1= p-q =1--------3
also eq 2 =p+q=7--------4
adding 3 and 4
p+q+p-q=7+1
2p=8
p=4
1/x=4
x=1/4
substituin x in eq 1
1/1/4-1/y=1
4-1/y=1
-1/y=1-4
-1/y=-3
1/y=3
y=1/3
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(2) Answer:
x = 1/2 , y = 1/3
Solution:
Given Equations Reducible to a Pair of Linear Equations in two variables :
2/x + 3/y = 13 ----(1)
5/x - 4/y = -2 ------(2)
If we substitute 1/x = a and 1/y = b , we get the following pair of linear
equations:
2a+3b=13 -----(3)
5a-4b = -2 -----(4)
Coefficients of b are 3 and 4 and
their LCM is 12 .
Using the elimination method .
Equation (3) × 4 8a+12b=52
Equation (4) × 3 15a-12b=-6
'b' terms have opposite sign , so we add the two equations.
23a = 46
=> a = 46/23
=> a = 2
Substitute the value of a in equation (3), we get
=> 2×2 +3b =13
=> 4 + 3b = 13
=> 3b = 13 - 4
=> 3b = 9
=> b = 9/3
=> b = 3
But 1/x = a = 2 => x = 1/2
1/y = b = 3 => y = 1/3
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Answer:
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