How do solve the following linear system?: $- 4 x + 9 y = 9, x - 3 y = - 6$ $-4x + 9y = 9 , x - 3y = -6$ ?

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Answer 1 · 2015-12-30T12:12:17

The solution for the system of equations is:

$x = 9, y = 5$ $color(blue)(x=9 ,y=5$

$- 4 x + 9 y = 9$ $color(blue)(-4x)+9y=9$ ..........equation $(1)$ $(1)$

$x - 3 y = - 6$ $x -3y=-6$ , multiplying by $4$ $4$
$4 x - 12 y = - 24$ $color(blue)(4x) -12y=-24$ .....equation $(2)$ $(2)$

Solving by elimination:
Adding both equations :

$cancelcolor(blue)(-4x)+9y=9$

$cancelcolor(blue)(4x) -12y=-24$

$-3y = -15$

$y=(-15)/(-3)$

$color(blue)(y=5$

Finding $x$ from equation $2$ :
$x -3y=-6$

$x =-6+3y$

$x =-6+3 xx 5$

$x =-6+15$

$color(blue)(x =9$

How do solve the following linear system?: -4x + 9y = 9 , x - 3y = -6 −4x+9y=9,x−3y=−6-4x + 9y = 9 , x - 3y = -6 ?