Question 1206264
<br>
{{{x*sqrt(2)+y*sqrt(3)=0}}}
{{{3x*sqrt(3)-5y*sqrt(2)=-38}}}<br>
One standard method for solving a pair of linear equations is elimination.  Multiply the first equation by sqrt(3) and the second by sqrt(2) (to make x a multiple of sqrt(6) in both equations):<br>
{{{x*sqrt(6)+3y=0}}}
{{{3x*sqrt(6)-10y=-38*sqrt(2)}}}<br>
Multiply the first of these equations by 3 and subtract one equation from the other to eliminate x and solve for y:<br>
{{{3x*sqrt(6)+9y=0}}}
{{{3x*sqrt(6)-10y=-38*sqrt(2)}}}
{{{19y=38*sqrt(2)}}}
{{{y=2*sqrt(2)}}}<br>
Substitute that value of y in the original first equation to solve for x:<br>
{{{x*sqrt(2)+2*sqrt(6)=0}}}
{{{x*sqrt(2)=-2*sqrt(6)}}}
{{{x=-2*sqrt(6)/sqrt(2)=-2*sqrt(3)}}}<br>
ANSWER: {{{x=-2*sqrt(3)}}}; {{{y=2*sqrt(2)}}}<br>