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Pair of Linear Equations in Two Variables
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28/05/2021 11:39 am
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Solve the pair of linear equations:
(a – b)x + (a + b) y = a2 – 2ab – b2
(a + b)(x + y) = a2 + b2
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28/05/2021 11:40 am
(a + b) y + (a – b) x = a2− 2ab − b2 …………… (i)
(x + y)(a + b) = a2 + b2
(a + b) y + (a + b) x = a2 + b2 ………………… (ii)
Subtracting equation (ii) from equation (i), we get
(a − b) x − (a + b) x = (a2 − 2ab − b2) − (a2 + b2)
x(a − b − a − b) = − 2ab − 2b2
− 2bx = − 2b (b + a)
x = b + a
Substituting this value in equation (i), we get
(a + b)(a − b) +y (a + b) = a2− 2ab – b2
a2 − b2 + y(a + b) = a2− 2ab – b2
(a + b) y = − 2ab
y = -2ab/(a+b)