# How do you determine the solution in terms of a system of linear equations for 5x-2y=22 and 9x+y=12?

May 5, 2018

$y = - 6$
$x = 2$

#### Explanation:

$5 x - 2 y = 22$ --- (1)
$9 x + y = 12$ --- (2)

From (2),
$9 x + y = 12$
$y = 12 - 9 x$ --- (3)

Sub (3) into (1)

$5 x - 2 \left(12 - 9 x\right) = 22$
$5 x - 24 + 18 x = 22$
$23 x = 46$
$x = 2$ --- (4)

Sub (4) into (3)
$y = 12 - 9 x$
$y = 12 - 9 \left(2\right)$
$y = 12 - 18$
$y = - 6$