If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form
(a) y – x = 0
(b) x + y = 0
Thinking Process
(i) Firstly, consider a linear equation ax + by + c = 0.
(ii) Secondly, substitute all points one by one and get three different equations.
(iii) Further, simplify the three equations and then substitute the values of a, b and c in the considered equation.
(b) Let us consider a linear equation ax + by + c = 0 … (i)
Since, (-2,2), (0, 0) and (2, -2) are the solutions of linear equation therefore it satisfies the Eq. (i), we get
At point(-2,2), -2a + 2b + c = 0 …(ii)
At point (0, 0), 0+0 + c = 0 => c = 0 …(iii)
and at point (2, – 2), 2a-2b + c = 0 …(iv)
From Eqs. (ii) and (iii),
c = 0 and – 2a + 2b + 0 = 0, – 2a = -2b,a = 2b/2 =>a = b
On putting a = b and c = 0 in Eq. (i),
bx + by + 0= 0=>bx + by = 0 => – b(x + y)= 0=>x + y = 0, b ≠ 0
Hence, x + y= 0 is the required form of the linear equation.
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