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=4Mathematics

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