# How do you solve 4x - 3y = 33 and x = - 4y - 25?

Apr 25, 2016

Point of intersection (lines cross) $\to \left(x , y\right) = \left(3 , - 7\right)$

#### Explanation:

Given:

$4 x - 3 y = 33$.................................(1)
$x = - 4 y - 25$.................................(2)

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$\textcolor{b l u e}{\text{Determine the common value of y}}$

Using equation (2) substitute for $x$ in equation (1)

$4 \left(- 4 y - 25\right) - 3 y = 33 \textcolor{w h i t e}{.} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$

$- 16 y - 100 - 3 y = 33$

$- 19 y - 100 = 33$

Multiply both sides by (-1)

$+ 19 y + 100 = - 33$

Subtract 100 from both sides

$19 y + 0 = - 133$

Divide both sides by 19

$\textcolor{b l u e}{y = - \frac{133}{19} = - 7}$
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$\textcolor{b l u e}{\text{Determine the common value of } x}$

Substitute the value of $y$ into equation (2)

color(brown)(x=-4y-25)" "color(green)( ->" " x=-4(-7)-25)

$\textcolor{b l u e}{x = + 3}$
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