Question

If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form ______.

Options

• y – x = 0

• x + y = 0

• –2x + y = 0

• –x + 2y = 0

Answer 1

If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form x + y = 0.

Explanation:

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 equation (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 equations (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 equation (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.