Question

Check which of the following are solutions of the equation $2x-y=6$ and which are not:
(i) $(3,0)$ (ii) $(0,6)$ (iii) $(2,-2)$ (iv) $(\sqrt{3},0)$

Answer 1

Equation is 2x - y = 6

(i) ( 3,0) i.e. x = 3, y = 0

Substituting the value of x and y in the equation

$2\times 3-0=6\Rightarrow 6-0=6$

6 = 6 which is true.

$\therefore (3,0)$ is a solution.

(ii) (0, 6) i.e. x = 0, y = 6

Substituting the value of x and y in the equation

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

$\Rightarrow -6=6$ which is not true.

$\therefore (0,6)$ is not a solution.

(iii) (2, -2) i.e. x = 2, y = -2

Substituting the value of x and y in the equation

$2\times 2-(-2)=6\Rightarrow 4+2=6$

$\Rightarrow 6=6$ which is true.

$\therefore (2,-2)$ is a solution.

(iv) $(\sqrt{3},0)i.e.x=\sqrt{3},y=0$

Substituting the value of x and y in the equation

$2\times \sqrt{3}-\left(0\right)=6\Rightarrow 2\sqrt{3}-0=6$

$\Rightarrow 2\sqrt{3}=6$ which is not true.

$\therefore (\sqrt{3},0)$ is not the solution.