Question

Question 12
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
C) -2x + y = 0
D) ​​​​​​​-x +2y = 0

Answer 1

The answer is 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, it satisfies the Eq, (i), we get;
At point (2, 2); -2a + 2b + c = 0 ....(ii)
At point (0, 0), 0 + 0 + c = 0 $\Rightarrow$ c = 0 ....(iii)
And at point (2, -2); 2a - 2b + c = 0 ....(iv)
From Equations (ii) and (iii),
c = 0 and -2a + 2b + 0 = 0, -2a = -2b,
$a=\frac{2b}{2}\Rightarrow$ a = b
On putting a = b and c = 0 in Eq. (i)
bx + by + 0 = $\Rightarrow$ bx + by = 0
$\Rightarrow$ b(x + y) = 0 $\Rightarrow$ x + y = 0, b $\ne$ 0
Hence, x + y = 0 is the required form of the linear equation.