Question 164969
Solve the following system for x and y:
{{{ sqrt(x)-2sqrt(y)=-1}}}
 {{{ 3sqrt(x)+4sqrt(y)=17}}}
:
Multiply the 1st equation by 2, add to the 2nd equation:
{{{ 2sqrt(x)-4sqrt(y)=-2}}}
 {{{ 3sqrt(x)+4sqrt(y)=17}}}
--------------------------------addition eliminates y, find x
{{{5sqrt(x) = 15 }}}
{{{sqrt(x) = (15/5)}}}; divide both sides by 5
{{{sqrt(x)}}} = 3
Square both sides
x = 9
:
Find y using the 1st equation, substitute 9 for x
{{{ sqrt(9)-2sqrt(y)=-1}}}
{{{ 3 - 2sqrt(y)=-1}}}
{{{-2sqrt(y)=-1-3}}}
 {{{-2sqrt(y)=-4}}}
Divide both sides by -2
{{{sqrt(y)=+2}}}
Square both sides
y = 4
:
:
Check solution in the 2nd original equation:
{{{ 3sqrt(9)+4sqrt(4)=17}}}
3(3) + 4(2)  = 17