SOLUTION: I need help solving this question: Solve the following system for x and y: {{{ sqrt(x)-2sqrt(y)=-1}}} {{{ 3sqrt(x)+4sqrt(y)=17}}}

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: I need help solving this question: Solve the following system for x and y: {{{ sqrt(x)-2sqrt(y)=-1}}} {{{ 3sqrt(x)+4sqrt(y)=17}}}       Log On

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Question 164969: I need help solving this question:
Solve the following system for x and y:
+sqrt%28x%29-2sqrt%28y%29=-1
+3sqrt%28x%29%2B4sqrt%28y%29=17

Found 2 solutions by ankor@dixie-net.com, Mathtut:
Answer by ankor@dixie-net.com(12695) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following system for x and y:
+sqrt%28x%29-2sqrt%28y%29=-1
+3sqrt%28x%29%2B4sqrt%28y%29=17
:
Multiply the 1st equation by 2, add to the 2nd equation:
+2sqrt%28x%29-4sqrt%28y%29=-2
+3sqrt%28x%29%2B4sqrt%28y%29=17
--------------------------------addition eliminates y, find x
5sqrt%28x%29+=+15+
sqrt%28x%29+=+%2815%2F5%29; divide both sides by 5
sqrt%28x%29 = 3
Square both sides
x = 9
:
Find y using the 1st equation, substitute 9 for x
+sqrt%289%29-2sqrt%28y%29=-1
+3+-+2sqrt%28y%29=-1
-2sqrt%28y%29=-1-3
-2sqrt%28y%29=-4
Divide both sides by -2
sqrt%28y%29=%2B2
Square both sides
y = 4
:
:
Check solution in the 2nd original equation:
+3sqrt%289%29%2B4sqrt%284%29=17
3(3) + 4(2) = 17

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
solve similtaneously: multiply top equation by -3 then add to 2nd equation
-3(+sqrt%28x%29-2sqrt%28y%29=-1) you get -3sqrt%28x%29%2B6sqrt%28y%29=+3
add to +3sqrt%28x%29%2B4sqrt%28y%29=17 and the x terms cancel out so you end up with 10sqrt%28y%29=20. now square both sides and you get 100y=400 y=4 plugin y=4 to either equation, I chose the 1st, to get find x. sqrt(x)-2sqrt(4)=-1 so sqrt(x)-2(2)=-1 and sqrt(x)=3 now square both terms to get rid of sqrt(x) and your left with x=9
answer: x=9
y=4