if 5u+3v=13uv and u-v=uv then (u,v)= (please, briefly explain the answer with elaborated steps) - Maths - Simultaneous Linear Equations

Question

if 5u+3v=13uv and u-v=uv then (u,v)=? (please, briefly explain the
answer with elaborated steps)

Rashi Lokwani · Accepted Answer

Dear Student,

5u + 3v = 13uvu-v = uv  Divide both equations by uv on both sides:5uuv + 3vuv = 13uvuv⇒5v + 3u = 13⇒3u + 5v = 13              
(1)   uuv - vuv = uvuv⇒1v - 1u = 1⇒- 1u + 1v = 1              
(2)  Let  1u = x and 1v=ySo, equations (1) and (2) become:3x + 5y = 13                     
(3)-x + y = 1                        
(4)   Multiply equation (4) by 3: 3(-x + y = 1) ⇒-3x + 3y = 3                   
(5)   Adding (3) and (5):8y = 16y = 168y = 2Substitue y = 2 in (4):-x + 2 = 1x = 2 - 1x = 1     Now, x = 1u⇒1 = 1u⇒u = 1andy = 1v⇒2 = 1v⇒v = 12 So, (u,v) = 1,12

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if 5u+3v=13uv and u-v=uv then (u,v)=? (please, briefly explain the answer with elaborated steps)