Question 187521
Solve: 
:
Assume the problem is:
{{{5x+3sqrt(y) = 13}}}
{{{2x-9sqrt(y) = 1}}}
:
Multiply the 1st equation by 3 and add
{{{15x + 9sqrt(y) = 39}}}
{{{2x - 9sqrt(y) = 1}}}
-----------------------eliminates y
17x = 40
x = {{{40/17}}}
:
Find y using the 1st equation
{{{5(40/17)+ 3sqrt(y) = 13}}}
{{{(200/17)+ 3sqrt(y) = 13}}}
{{{3sqrt(y) = 13 - (200/17)}}}
{{{3sqrt(y) = (221/17)- (200/17)}}}
{{{3sqrt(y) = (21/17)}}}
Divide both sides by 3
{{{sqrt(y) = (7/17)}}}
Square both sides
y = {{{49/221}}}
;
Check solution; x = {{{40/17}}}, y = {{{49/221}}} in the 2nd equation
{{{2x-9sqrt(y) = 1}}}
{{{2(40/17)- 9sqrt(49/221) = 1 }}}
{{{(80/17)- 9*(7/17) = 1}}}
{{{(80/17)- (63/17) = 1}}}
{{{17/17}}} = 1