Question #dfe7b

Mar 24, 2017

$\left(3 , 0\right)$

Explanation:

Label the equations.

$\textcolor{red}{y} = - 2 x + 6 \to \left(1\right)$

$\textcolor{red}{y} = x - 3 \to \left(2\right)$

Since both equation have y as the subject we can equate the right sides.

$\Rightarrow x - 3 = - 2 x + 6$

$x + 2 x - 3 = \cancel{- 2 x} \cancel{+ 2 x} + 6$

$\Rightarrow 3 x - 3 = 6$

$3 x \cancel{- 3} \cancel{+ 3} = 6 + 3$

$\Rightarrow 3 x = 9$

divide both sides by 3

$\frac{\cancel{3} x}{\cancel{3}} = \frac{9}{3}$

$\Rightarrow x = 3$

Substitute this value into either of the 2 equations.

$\text{Substitute "x=3" in } \left(2\right)$

$x = 3 \to y = 3 - 3 = 0$

$\textcolor{b l u e}{\text{As a check}}$

$\text{Substitute " x=3" in } \left(1\right)$

$x = 3 \to \left(- 2 \times 3\right) + 6 = - 6 + 6 = 0 \to \text{ true}$

$\Rightarrow \left(3 , 0\right) \text{ is the point of intersection}$
graph{(y+2x-6)(y-x+3)=0 [-10, 10, -5, 5]}