Question

Root 2x - root 3y = 0
Root 5x + root 2y = 0

Answer 1

$\begin{gathered} \sqrt{2x} - \sqrt{3y} = 0 \\ \\ \sqrt{2x} = \sqrt{3y} \\ \\ squaring \: both \: side \\ \\ 2x = 3y \\ \\ 2x - 3y = 0 \: \: \: eq1 \\ \\ \sqrt{5x} + \sqrt{2y} = 0 \\ \\ squaring \: both \: side \\ \\ \sqrt{5x} = - \sqrt{2y} \\ \\ 5x = 2y \\ \\ 5x - 2y = 0 \: \: \: eq2 \\ \\ \end{gathered}$

From eq 1 and eq2

multiply eq 1 by 5 and eq2 by 2 and subtract both

$\red{\begin{gathered}10x - 9y = 0 \\ 10x - 4y = 0 \\ - \: \: \: + \: \: \: \: \\ - 5y = 0 \\\\\ y = \frac{ - 0}{5} \\ \\ y = 0 \\ \\ \end{gathered}}$

y=0

put value of y in eq 1

$\begin{gathered}2x - 3(0) = 0 \\ \\ 2x = 0 \\ \\ x = \frac{0}{2} \\ \\ x = 0 \\ \end{gathered}$

x=0

So, x= 0

y=0

Answer 2

Solution:


From eq 1 and eq2

multiply eq 1 by 5 and eq2 by 2 and subtract both


put value of y in eq 1


So, x= 0

y= 0

Hope it helps you.