# How do you solve 7x + 6y = 1 and x = 7 - 2y using substitution?

Apr 24, 2016

Point of intersection$\text{ } \to \left(x , y\right) = \left(- 5 , 6\right)$

#### Explanation:

Given:

$x = 7 - 2 y$ ............................(1)
$7 x + 6 y = 1$ .........................(2)

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Substitute for $x$ in equation (2) using equation (1)

$\implies 7 x + 6 y = 1 \text{ "->" } 7 \left(7 - 2 y\right) + 6 y = 1$

$49 - 14 y + 6 y = 1$

$49 - 8 y = 1$

$8 y = 48$

$y = \frac{48}{8} = 6$

$\textcolor{b l u e}{y = 6}$
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Substitute for $y$ in equation (1)

$x = 7 - 2 y \text{ "->" } x = 7 - 2 \left(6\right)$

$\textcolor{b l u e}{x = - 5}$
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