Question

reduce the following into linear equations in two variables 5/x+2y -7/x+2y =10 and 3/ x+2y + 8/x+2y=12​

Answer 1

Answer:

$\mathrm{\frac{5}{x}+2y-\frac{7}{x}+2y=10,\:\frac{3}{x}+2y+\frac{8}{x}+2y=12\quad :\quad x=\frac{13}{2},\:y=\frac{67}{26},\:\quad \:y\ne \frac{5}{2},\:x\ne \:0}$

Step-by-step explanation:

$\mathrm{\begin{bmatrix}\frac{5}{x}+2y-\frac{7}{x}+2y=10 \\\\\ \frac{3}{x}+2y+\frac{8}{x}+2y=12\end{bmatrix}}$

$\mathrm{Substitute\:x=-\frac{1}{5-2y}}$

$\mathrm{\begin{bmatrix}\frac{3}{-\frac{1}{5-2y}}+2y+\frac{8}{-\frac{1}{5-2y}}+2y=12\end{bmatrix}}$

$\mathrm{\begin{bmatrix}26y-55=12\end{bmatrix}}$

$\mathrm{For\:}x=-\frac{1}{5-2y}$

$\mathrm{Substitute\:}y=\frac{67}{26}$

$x=-\frac{1}{5-2\cdot \frac{67}{26}}$

$x=\frac{13}{2}$

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

$x=\frac{13}{2},\:y=\frac{67}{26},\:\quad \:y\ne \frac{5}{2},\:x\ne \:0$