Question

Check which of the following are solutions of the equation 2x − 3y = 6.
(i) (3, 0)
(ii) (0, 2)
(iii) (2, 6)
(iv) (6, 2)

Answer 1

(i) $(3,0)$
Given equation: $2x-3y=6$
Putting $x=3,y=0$ in the given equation, we get:
$LHS=2\times 3-3\times 0=6=RHS$
So, it satisfies the given equation.

(ii) $(0,2)$
Given equation: $2x-3y=6$
Putting $x=0,y=2$ in the given equation, we get:
$LHS\hspace{0.17em}=2\times 0-3\times 2=-6$ ≠ $RHS$
So, it does not satisfy the given equation.

(iii) $(2,6)$
Given equation: $2x-3y=6$
Putting $x=2,y=6$ in the given equation, we get:
$LHS=2\times 2-3\times 6=-14$ ≠ $RHS$
So, it does not satisfy the given equation.

(iv) $(6,2)$
Given equation: $2x-3y=6$
Putting $x=6,y=2$ in the given equation, we get:
$LHS=2\times 6-3\times 2=12-6=6=RHS$
So, it satisfies the given equation.

Hence, $(3,0),(6,2)$ are the solutions of the given equation.