# If a linear equation has solutions (-2, 2),

Question:

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.

Solution:

(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.