How do solve the following linear system?: $- 9 x + 5 y = 16, x - 3 y = - 6$ $-9x + 5y = 16 , x - 3y = -6$ ?

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Answer 1 · 2016-05-10T08:19:02

The solution for the system of equations is:
$x = \frac{- 9}{11}$ $color(blue)(x = (- 9 )/ 11$

$y = \frac{19}{11}$ $color(blue)(y = 19 / 11$

$- 9 x + 5 y = 16$ $color(green)(- 9x) + 5y = 16$ ..............equation $(1)$ $(1)$

$x - 3 y = - 6$ $x - 3y = - 6$ , multiplying by $9$ $9$
$9 x - 27 y = - 54$ $color(green)(9x) - 27y = - 54$ ............equation $(2)$ $(2)$

Solving by elimination:

Adding equations $1$ $1$ and $2 :$ $2:$

$cancelcolor(green)(- 9x) + 5y = 16$
$cancelcolor(green)(9x) - 27y = - 54$

$-22y = -38$

$y = (-38) / (-22)$

$color(blue)(y = 19 / 11$

Finding $x$ from equation $2:$

$x - 3y = - 6$

$x = - 6 + 3y$

$x = - 6 + 3 * (19 / 11)$

$x = - 6 + 57 / 11$

$x = (- 66 + 57 )/ 11$

$color(blue)(x = (- 9 )/ 11$

How do solve the following linear system?: -9x + 5y = 16 , x - 3y = -6 −9x+5y=16,x−3y=−6-9x + 5y = 16 , x - 3y = -6 ?