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

Feb 1, 2016

$\textcolor{b l u e}{y = - 27}$
$\textcolor{b l u e}{x = 39}$

#### Explanation:

Given:

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

Two equations; two unknowns thus solvable

$\textcolor{b l u e}{\text{Method:}}$

$\textcolor{b r o w n}{\text{Eliminate one of the unknowns by substitution, so that we are }}$$\textcolor{b r o w n}{\text{solving for 1 unknown in 1 equation.}}$

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$\textcolor{b l u e}{\text{To find the value of } x}$

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

$9 \left(- x + 12\right) = - 3 x - 9 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left({2}_{a}\right)$

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

Collecting like terms we have

$9 x - 3 x = 108 + 9$

$3 x = 117$

Divide both sides by 3 giving:

$\textcolor{b l u e}{x = 39}$........................................(3)

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$\textcolor{b l u e}{\text{To find the value of } y}$

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

$y = - \left(39\right) + 12 = - 27$

$\textcolor{b l u e}{y = - 27}$