Question

Solve the pair of equations \( \sqrt{2} x + \sqrt{3}y = 0 \) and \( \sqrt{3}x - \sqrt{8}y = 0 \) by the method of substitution or elimination.

Hint:

For equations with square roots, eliminate them by multiplying appropriately.

Answer 1

Using elimination, multiply the first equation by \( \sqrt{3} \) and the second by \( \sqrt{2} \):
\[ \sqrt{6} x + 3y = 0. \] \[ \sqrt{6} x - 2\sqrt{2} y = 0. \] Subtracting:
\[ (3y + 2\sqrt{2} y) = 0. \] \[ y(3 + 2\sqrt{2}) = 0. \] \[ y = 0. \] Substituting in \( \sqrt{2} x + \sqrt{3} y = 0 \):
\[ \sqrt{2} x = 0 \Rightarrow x = 0. \] \[ (x, y) = (0,0). \]