Question

Check which of the following are solutions of an equation $x+2y=4$?
(i) (0, 2) (ii) (2, 0) (iii) (4, 0) (iv) ($\sqrt{2},-3\sqrt{2}$) (v) (1, 1) (vi) (-2, 3)

Answer 1

Given equation is$x+2y=4$

(i) Put the value x=0 and y=2 we get

$0+2\times 2=4$

$\Rightarrow 4=4$

Then both sides are equal then (0,2) is the solution of equation x+2y=4

(ii) Put the value x=2 and y=0 we get

$2+2\times 0=4$

$\Rightarrow 2\ne 4$

Then both sides are not equal then (0,2) is not the solution of equation

x+2y=4

(iii) Put the value x=4 and y=0 we get

$4+2\times 0=4$

$\Rightarrow 4=4$

Then both sides are equal then (4,0) is the solution of equation x+2y=4

(iv)$x+2y=4$

Put $x=\sqrt{2},y=-3\sqrt{2}$ we get

$\sqrt{2}+2(-3\sqrt{2})=4$

$\Rightarrow \sqrt{2}-3\sqrt{2}=4$

$\Rightarrow -2\sqrt{2}\ne 4$

Then both sides are not equal then $(\sqrt{2},-3\sqrt{2})$ is not the solution of equation

x+2y=4

(v) Put the value x=1 and y=1 we get

$1+2\times 1=4$

$\Rightarrow 3\ne 4$

Then both sides are not equal then (1,1) is not the solution of equation

x+2y=4

(vi) Put the value x=-2 and y=3 we get

$-2+2\times 3=4$

$\Rightarrow 4=4$

Then both sides are equal then (-1,3) is the solution of equation

x+2y=4