Question

If a linear equation has solutions $\left(-2,2\right),\left(0,0\right)$ and $\left(2,-2\right)$ then its of the form:

• A. $y-x=0$
• B. $x+y=0$
• C. $-2x+y=0$
• D. $-x+2y=0$

Answer 1

The correct option is B

$x+y=0$

Explanation for correct option :

Option $\left(B\right)\mathbf{:}$$x+y=0$

On solving equation $x+y=0$ by keeping solution $\left(-2,2\right)$

$\Rightarrow -2+2=0$

Thus, the solution $\left(-2,2\right)$ satisfies the equation $x+y=0$

On solving equation $x+y=0$ by keeping solution $\left(0,0\right)$

$\Rightarrow -0+0=0$

Thus, the solution $\left(0,0\right)$satisfies the equation $x+y=0$

On solving equation $x+y=0$ by keeping solution $\left(2,-2\right)$

$\Rightarrow 2+\left(-2\right)=0$

Thus, the solution $\left(2,-2\right)$ satisfies the equation $x+y=0$

Hence, the linear equation with solution $\left(-2,2\right)$,$\left(0,0\right)$,$\left(2,-2\right)$ is in form $x+y=0$ .

Explanation for Incorrect option:

Option $\left(A\right)$:

On solving equation $y-x=0$ by keeping solution $\left(-2,2\right)$

$\Rightarrow 2-\left(-2\right)=0$

$\Rightarrow 4=0$

Hence, the solution $\left(-2,2\right)$ does not satisfies the equation $y-x=0$

On solving equation $y-x=0$by keeping solution $\left(0,0\right)$

$\Rightarrow 0-0=0$

Hence, the solution $\left(0,0\right)$satisfies the equation $y-x=0$

On solving equation $y-x=0$ by keeping solution $\left(2,-2\right)$

$\Rightarrow -2-2=0\Rightarrow -4=0$

Hence, the solution $\left(2,-2\right)$ does not satisfies the equation $y-x=0$

Thus, the linear equation with solution $\left(2,-2\right)$ and $\left(-2,2\right)$is not in form of $y-x=0$.

Option $\left(C\right)$:

On solving equation $-2x+y=0$ by keeping solution $\left(-2,2\right)$

$\Rightarrow -2\left(-2\right)+2=0\Rightarrow -4+2=0$

Hence, the solution $\left(-2,2\right)$ does not satisfies the equation $-2x+y=0$

On solving equation $-2x+y=0$ by keeping solution $\left(0,0\right)$

$\Rightarrow -2\left(0\right)+0=0$

Hence, the solution $\left(0,0\right)$satisfies the equation $-2x+y=0$

On solving equation $-2x+y=0$ by keeping solution $\left(2,-2\right)$

$\Rightarrow -2\left(2\right)+\left(-2\right)=0$

$\Rightarrow -4-2=0\Rightarrow -6=0$

Hence, the solution $\left(2,-2\right)$ does not satisfies the equation $-2x+y=0$

Thus, the linear equation with solution $\left(2,-2\right)$ and $\left(-2,2\right)$is not in form of $-2x+y=0$.

Option $\left(D\right)$:

On solving equation $-x+2y=0$ by keeping solution $\left(-2,2\right)$

$\Rightarrow -2+2\left(2\right)=0$

$\Rightarrow 2=0$

Hence, the solution $\left(-2,2\right)$ does not satisfies the equation $-x+2y=0$

On solving equation $-x+2y=0$ by keeping solution $\left(0,0\right)$

$\Rightarrow -0+2\left(0\right)=0$

Hence, the solution $\left(0,0\right)$satisfies the equation $-x+2y=0$

On solving equation $-x+2y=0$ by keeping solution $\left(2,-2\right)$

$\Rightarrow -2+2\left(-2\right)=0$

$\Rightarrow -6=0$

Hence, the solution $\left(2,-2\right)$ does not satisfies the equation $-x+2y=0$

Thus, the linear equation with solution $\left(2,-2\right)$ and $\left(-2,2\right)$is not in form of $-x+2y=0$.

Therefore, Option $\left(B\right)$ is correct answer.