Question

2/x+1/y=16, 3/x-2/y=-1 (simultaneous equations)​

Answer 1

Answer:

$\frac{2}{x}+\frac{1}{y}=16,\:\frac{3}{x}-\frac{2}{y}=-1\quad :\quad x=\frac{7}{31},\:y=\frac{7}{50},\:\quad \:y\ne \frac{1}{16},\:x\ne \:0,\:y\ne \:0$

Step-by-step explanation:

$\begin{bmatrix}\frac{2}{x}+\frac{1}{y}=16\\ \frac{3}{x}-\frac{2}{y}=-1\end{bmatrix}$

$\mathrm{Substitute\:}x=-\frac{2y}{1-16y}$

$\begin{bmatrix}\frac{3}{-\frac{2y}{1-16y}}-\frac{2}{y}=-1\end{bmatrix}$

$\begin{bmatrix}\frac{48y-7}{2y}=-1\end{bmatrix}$

$\mathrm{For\:}x=-\frac{2y}{1-16y}$

$\mathrm{Substitute\:}y=\frac{7}{50}$

$x=-\frac{2\cdot \frac{7}{50}}{1-16\cdot \frac{7}{50}}$

$x=\frac{7}{31}$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=\frac{7}{31},\:y=\frac{7}{50},\:\quad \:y\ne \frac{1}{16},\:x\ne \:0,\:y\ne \:0$