Question 52885: Solve the system of equations: (hint: let (1/x)=t and (1/y)=u)
(2/x)+(1/y)=11
(3/x)-(5/y)=10
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! (2/x)+(1/y)=11
(3/x)-(5/y)=10
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2(1/x)+(1/y)=11
3(1/x)-5(1/y)=10
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Let 1/x=t and 1/y=u
2t+u=11
3t-5u=10
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Solve the first equation for u, substitute it for u in the second equation and solve for t.
2t+u=11
-2t+2t+u=-2t+11
u=-2t+11
3t-5(-2t+11)=10
3t+10t-55=10
13t-55=10
13t-55+55=10+55
13t=65
13t/13=65/13
t=5
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Substitute that answer for t in the first equation and solve for u.
2(5)+u=11
10+u=11
-10+10+u=11-10
u=1
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Only we were supposed to find x and y not t and u, so let t=1/x and u=1/y and solve for x and y.
t=5 becomes 1/x=5
x(1/x)=5x
1=5x
1/5=5x/5
1/5=x
u=1 becomes 1/y=1
y(1/y)=1(y)
1=y
Therefore, our answer is (x,y)=(1/5,1)
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