# How do you solve the following system: -29=5y-3x, 4x-5y= -1 ?

Jan 17, 2018

Solve the former one first
$- 29 = 5 y - 3 x$
Solve for $y$
Transfer $3 x$
$3 x - 29 = 5 y$
You can also transfer the $5$ in $5 y$ but that would be stupid considering that the next equation wants $5 y$
The latter equation
$4 x - 5 y = - 1$
Put the value of $5 y$
$4 x - \left(3 x - 29\right) = - 1$
Which gives us
$4 x - 3 x + 29 = - 1$
Solve
$x + 29 = - 1$
Transfer the $- 1$
$x + 29 + 1 = 0$
$x + 30 = 0$
Which gives
$x = - 30$
$5 y = 3 x - 29$
Put value of $x$
$5 y = 3 \times \left(- 30\right) - 29$
Solve
$5 y = - 90 - 29$
Solve
$5 y = - 119$
Transfer $5$
$y = - \frac{119}{5}$
Or...
$y = - 23.8$