Answer to Question #291939 in Algebra for Rossy

Question

Solve the pair of equation 2y^-1 -3z^-1=4 and 4y^-1+z^-1=1

Answer 1

Let us change the variables: x = 1/y, t = 1/z. Therefore, our equations take form

$\begin{cases} 2x -3t = 4, \\ 4x + t = 1. \end{cases}$

From the second equation we obtain $t = 1-4x.$ Next, we substitute it in the first equation and obtain

$2x - 3(1-4x) = 4, \\ 14x = 7, \\ x = 0.5$

Therefore, $t = 1-4\cdot 0.5 = -1.$

$y = 1/x = 1/0.5 = 2, \\ z = 1/t = 1/(-1) = -1.$