How do you solve this system of equation: 5x - 6y = 9 and 9- 3y = - x?

Nov 13, 2017

$\left(x , y\right) \to \left(9 , 6\right)$

Explanation:

$5 x - 6 y = 9 \to \left(1\right)$

$9 - 3 y = - x \to \left(2\right)$

$\text{rearrange equation "(2)" to give x in terms of y}$

$\text{multiply through by } - 1$

$- 9 + 3 y = x \to \left(3\right)$

$\textcolor{b l u e}{\text{substitute "x=3y-9" into equation }} \left(1\right)$

$5 \left(3 y - 9\right) - 6 y = 9$

$\Rightarrow 15 y - 45 - 6 y = 9$

$\Rightarrow 9 y - 45 = 9$

$\text{add 45 to both sides}$

$9 y \cancel{- 45} \cancel{+ 45} = 9 + 45$

$\Rightarrow 9 y = 54$

$\text{divide both sides by 9}$

$\frac{\cancel{9} y}{\cancel{9}} = \frac{54}{9}$

$\Rightarrow y = 6$

$\text{substitute this value into equation } \left(3\right)$

$\Rightarrow x = - 9 + \left(3 \times 6\right) = - 9 + 18 = 9$

$\text{point of intersection } = \left(9 , 6\right)$
graph{(y-5/6x+3/2)(y-1/3x-3)((x-9)^2+(x-6)^2-0.05)=0 [-20, 20, -10, 10]}