How do you solve the following system?: $9y = -3x - 9 , y=-x + 12$

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Answer 1 · 2016-02-01T16:35:08

$color(blue)(y=-27)$
$color(blue)(x= 39)$

Given:

$9y=-3x-9$ ..........................(1)
$y=-x+12$ ............................(2)

Two equations; two unknowns thus solvable

$color(blue)("Method:")$

$color(brown)("Eliminate one of the unknowns by substitution, so that we are ")$ $color(brown)("solving for 1 unknown in 1 equation.")$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To find the value of "x)$

Substitute equation (2) into equation (1) giving:

$9(-x+12)=-3x-9" "......................(2_a)$

$-9x+108=-3x-9$

Collecting like terms we have

$9x-3x=108+9$

$3x=117$

Divide both sides by 3 giving:

$color(blue)(x= 39)$ ........................................(3)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To find the value of "y)$

Substitute equation (3) into equation (2) (the easier of the two!)

$y=-(39)+12 = -27$

$color(blue)(y=-27)$

How do you solve the following system?: 9y = -3x - 9 , y=-x + 12 9y = -3x - 9 , y=-x + 12