The solution of the equations √3x – √7y = 0 and √8x + √3y =

1.	The solution of the equations √3x – √7y = 0 and √8x + √3y = 0 is ………………A) x = 3, y = 7 B) x = 8, y = 3 C) x = 0, y = 1 D) x = 0, y = 0
Answer» Correct option is (D) x = 0, y = 0 Given equations are \(\sqrt3x – \sqrt7y = 0\) _________(1) and \(\sqrt8x + \sqrt3y = 0\) _________(2) Multiply equation (1) by \(\sqrt3\) and equation (2) by \(\sqrt7,\) we get \(3x–\sqrt{21}y = 0\) _________(3) \(\sqrt{56}x+\sqrt{21}y = 0\) _________(4) By adding equations (3) & (4), we obtain \((3x-\sqrt{21}y)+(\sqrt{56}x+\sqrt{21}y)\) = 0+0 \(\Rightarrow\) \(3x+\sqrt{56}x=0\) \(\Rightarrow\) \((3+\sqrt{56})x=0\) \(\Rightarrow\) x = 0 \((\because3+\sqrt{56}\neq0)\) Put x = 0 in equation (3), we get \(\sqrt3\times0-\sqrt7y = 0\) \(\Rightarrow\) \(0-\sqrt7y = 0\) \(\Rightarrow\) \(\sqrt7y = 0\) \(\Rightarrow\) \(y=\frac0{\sqrt7}=0\) Hence, solution of given equations is x = 0, y = 0. Correct option is D) x = 0, y = 0

The solution of the equations √3x – √7y = 0 and √8x + √3y = 0 is ………………A) x = 3, y = 7 B) x = 8, y = 3 C) x = 0, y = 1 D) x = 0, y = 0

Answer»

Correct option is (D) x = 0, y = 0

Given equations are

\(\sqrt3x – \sqrt7y = 0\) _________(1)

and \(\sqrt8x + \sqrt3y = 0\) _________(2)

Multiply equation (1) by \(\sqrt3\) and equation (2) by \(\sqrt7,\) we get

\(3x–\sqrt{21}y = 0\) _________(3)

\(\sqrt{56}x+\sqrt{21}y = 0\) _________(4)

By adding equations (3) & (4), we obtain

\((3x-\sqrt{21}y)+(\sqrt{56}x+\sqrt{21}y)\) = 0+0

\(\Rightarrow\) \(3x+\sqrt{56}x=0\)

\(\Rightarrow\) \((3+\sqrt{56})x=0\)

\(\Rightarrow\) x = 0 \((\because3+\sqrt{56}\neq0)\)

Put x = 0 in equation (3), we get

\(\sqrt3\times0-\sqrt7y = 0\)

\(\Rightarrow\) \(0-\sqrt7y = 0\)

\(\Rightarrow\) \(\sqrt7y = 0\)

\(\Rightarrow\) \(y=\frac0{\sqrt7}=0\)

Hence, solution of given equations is x = 0, y = 0.

Correct option is D) x = 0, y = 0