Alg3.1.9

Find the solution such that u,v not equal to zero in $2u+v=\frac{7}{3}uv,u+3v=\frac{11}{3}uv\,$

Given $2u+v=\frac{7}{3}uv,u+3v=\frac{11}{3}uv\,$

Multiplying the second equation by 2 and subtracting we get

$(2u+v-\frac{7}{3}uv)-(2u+6v-\frac{22}{3})=0\,$

$-5v+\frac{15}{3}uv=0\,$

$-5v=-5uv,u=1\,$

Substituting this value in equation one,we get

$2(1)+v=\frac{7}{3}v\,$

$2=\frac{4}{3}v,v=\frac{3}{2}\,$

Therefore the solution is $u=1,v=\frac{3}{2}\,$