How do solve the following linear system?: $4 x + 2 y = 6, 3 x + y = - 20$ $4x+2y=6 , 3x + y = -20$ ?

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Answer 1 · 2016-05-22T15:23:54

The solution for the system of equations is:

$x = - 23$ $color(green)(x = -23$

$y = 49$ $color(green)(y =49$

$4 x + 2 y = 6$ $4x + color(blue)(2y) = 6$ ..............equation $(1)$ $(1)$
$3 x + y = - 20$ $3x + y =- 20$ , multiplying by $2$ $2$

$6 x + 2 y = - 40$ $6x + color(blue)( 2y) =- 40$ ......equation $(2)$ $(2)$

Solving by elimination:

Subtracting equation $2$ $2$ from equation $1$ $1$ :

$4x + cancelcolor(blue)(2y) = 6$

$-6x - cancelcolor(blue)( 2y) =40$

$-2x = 46$

$x = 46 /(-2)$

$color(green)(x = -23$

Finding $y$ from equation $2:$
$3x + y =- 20$

$y =- 20 - 3x$

$y =- 20 - 3 xx (-23)$

$y =- 20 + 69$

$color(green)(y =49$

How do solve the following linear system?: 4x+2y=6 , 3x + y = -20 4x+2y=6,3x+y=−20 4x+2y=6 , 3x + y = -20 ?