# How do you solve the following system: 7x-2y= -67, x+3y=3 ?

Feb 5, 2016

$x = 10 \frac{5}{19} \text{ }$ I will let the reader solve for $y$. Approach given.

#### Explanation:

Given:
$7 x - 2 y = - 67$.................................(1)
$x + 3 y = 3$............................................(2)
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Rewrite equation (2) to give:

$y = - \frac{1}{3} x + 1 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left({2}_{a}\right)$
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Substitute $\left({2}_{a}\right)$ into (1) giving:

$7 x - 2 \left(- \frac{1}{3} x + 1\right) = - 67 \text{ } \ldots . \left({1}_{a}\right)$
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$\textcolor{b l u e}{\text{Solving for } x}$

$7 x + \frac{2}{3} x - 2 = - 67$

$\frac{19}{3} x = - 65$

$\textcolor{b l u e}{x = - \frac{195}{19} \text{ } \to 10 \frac{5}{19}}$

$\textcolor{p u r p \le}{\text{Notice how I keep fractional values instead of decimals.}}$$\textcolor{p u r p \le}{\text{It is more precise that way!}}$
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I will let you solve for $y$. Just substitute the value for $x \text{ in } \left({2}_{a}\right)$
$\left({2}_{a}\right)$ looks as though it is the simplest one to use!