Question

Solve the following pair of equations:

$\frac{2x+y}{x+y}=\frac{3}{2}and\frac{x-y}{2x-y}=\frac{-3}{10},x+y\ne 0,2x-y\ne 0$

Answer 1

Given equations

$\frac{2x+y}{x+y}=\frac{3}{2};\frac{x-y}{2x-y}=\frac{-3}{10}$

Let $4x+2y=3x+3y;10x-10y+6x-3y=0$

$\Rightarrow x-y=0⟶\left(1\right),16x+13y=0\Rightarrow x-\frac{13}{16}y=0\Rightarrow ⟶\left(2\right)$

Subtracting $\left(1\right)$ and $\left(2\right)$

$x-3y=0x-\frac{13}{16}y=0--------[\left(\frac{13}{16}\right)-1]y=0$

$y=0,x=0$

But it is not possible as given in the question $x+y\ne 0$

Therefore No solution.