# How do you solve 8x + 7y = 25 and x = 25 - 4y  using substitution?

Mar 5, 2018

$\left(x , y\right) \to \left(- 3 , 7\right)$

#### Explanation:

$8 x + 7 y = 25 \to \left(1\right)$

$x = 25 - 4 y \to \left(2\right)$

$\text{substitute "x=25-4y" into equation } \left(1\right)$

$8 \left(25 - 4 y\right) + 7 y = 25$

$\Rightarrow 200 - 32 y + 7 y = 25$

$\Rightarrow 200 - 25 y = 25$

$\text{subtract 200 from both sides}$

$\cancel{200} \cancel{- 200} - 25 y = 25 - 200$

$\Rightarrow - 25 y = - 175$

$\text{divide both sides by } - 25$

$\frac{\cancel{- 25} y}{\cancel{- 25}} = \frac{- 175}{- 25}$

$\Rightarrow y = 7$

$\text{substitute " y=7" into equation } \left(2\right)$

$x = 25 - \left(4 \times 7\right) = 25 - 28 = - 3$

$\Rightarrow \text{point of intersection } = \left(- 3 , 7\right)$