SOLUTION: Solve the system of equations: (hint: let (1/x)=t and (1/y)=u) (2/x)+(1/y)=11 (3/x)-(5/y)=10

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
----------------
2(1/x)+(1/y)=11
3(1/x)-5(1/y)=10
------------------
Let 1/x=t and 1/y=u
2t+u=11
3t-5u=10
-------------------
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
----------------------------
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
-----------------------------
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)
RELATED QUESTIONS
Solve the system. Hint 1/x =t , 1/y =u , 1/z =w. 2/x +2/y -2/z =-1 2/x -10/y +5/2 =4... (answered by richwmiller)

Solve the system to find (u,v). Hint: x = 1/u and y = 1/v. Use x and y in the... (answered by ewatrrr)

I have been working on this problem and I still can't seem to get it. I was wondering if... (answered by checkley77)

The following system of equations is not linear. If you substitute u for 1/x and v for... (answered by Fombitz)

solve the system of equations by graphing. y = -3/5 x y=-1/5x... (answered by htmentor)

Solve the system of equations { y = x + 1 { y = -4x + 11 --------------- x, y ( , ) (answered by asuar010)

Solve the system of THREE Equations 4x+y+2z = 10 y = x-1 x=5 Thanks (answered by Alan3354)

solve each system of equations algebraically 1/x + 3/y = 6 2/x -1/y =... (answered by stanbon)