Question

Question 3
Check which of the following are solutions of the equation $x-2y=4$ and which are not:
$\left(i\right)(0,2)\left(ii\right)(2,0)\left(iii\right)(4,0)\left(iv\right)(\surd 2,4\surd 2)\left(v\right)(1,1)$

Answer 1

(i) Put $x=0andy=2$ in the equation $x-2y=4.$
$0-2\times 2=-4$
$\Rightarrow -4\ne 4$
$\therefore (0,2)$ is not a solution of the given equation.
(ii) Put $x=2andy=0$ in the equation $x-2y=4.$
$2-2\times 0=2$
$\Rightarrow 2\ne 4$
$\therefore (2,0)$ is not a solution of the given equation.
(iii) Put $x=4andy=0$ in the equation $x-2y=4.$
$4-2\times 0=4$
$\Rightarrow 4=4$
$\therefore (4,0)$ is a solution of the given equation.
$\left(iv\right)Putx=\surd 2andy=4\surd 2$ in the L.H.S equation $x-2y=4.$
$\surd 2-2\times 4\surd 2=\surd 2-8\surd 2=\surd 2(1-8)=-7\surd 2$
$\Rightarrow -7\surd 2\ne 4$
$\therefore (\surd 2,4\surd 2)$ is not a solution of the given equation.
(v) Put $x=1andy=1$ in the equation $x-2y=4.$
$1-2\times 1=-1$
$\Rightarrow -1\ne 4$
$\therefore (1,1)$ is not a solution of the given equation.