# How do you solve the system by graphing 3x + 5y = -8 and 8x - 2y = -6?

May 18, 2017

Point of intersection $\to \left(x , y\right) = \left(- 1 , - 1\right)$

#### Explanation:

Given:

$8 x - 2 y = - 6 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$
$3 x + 5 y = - 8 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(2\right)$
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$\textcolor{b l u e}{\text{Consider } E q u a t i o n \left(1\right)}$

$\textcolor{b r o w n}{\text{Showing all the steps}}$

Add $2 y$ to both sides

$8 x = - 6 + 2 y$

$8 x + 6 = 2 y$

Divide both sides by 2

$4 x + 3 = y$

$y = 4 x + 3 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left({1}_{a}\right)$
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$\textcolor{b l u e}{\text{Consider } E q u a t i o n \left(2\right)}$

Using the same processes as above. I have and NOT showing all the steps:

$y = - \frac{3}{5} x - \frac{8}{5} \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . E q u a t i o n \left({2}_{a}\right)$
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By substituting values for $x$ build a table of values for each equation. You only need as a minimum 2 points for each line. 3 is better as it forms a check. You lines should pass through each point.