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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)


Solution

 Given equation is$$x+2y=4$$
(i) Put the value x=0 and y=2 we get
$$0+2\times 2=4$$
$$\Rightarrow4=4$$
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
$$2+2\times 0=4$$
$$\Rightarrow 2\neq 4$$ 
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
$$4+2\times 0=4$$
$$\Rightarrow4=4$$
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
$$\sqrt{2}+2(-3\sqrt{2})=4$$
$$\Rightarrow \sqrt{2}-3\sqrt{2}=4$$
$$\Rightarrow -2\sqrt{2}\neq 4$$ 
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
$$1+2\times 1=4$$
$$\Rightarrow 3\neq 4$$ 
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


Mathematics

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