Question

Solve using elimination or substitution method

Answer 1

$\left\{\begin{array}{ccc}y=\dfrac{2}{3}x+3\\2x-3y=-9\end{array}\right\\\\\text{substitute}\ y=\dfrac{2}{3}x+3\ \text{to the second equation}\\\\2x-3\left(\dfrac{2}{3}x+3\right)=-9\qquad|\text{use distributive property}\\\\2x+(-3)\left(\dfrac{2}{3}x\right)+(-3)(3)=-9\\\\2x-2x-9=-9\qquad|\text{add 9 to both sides}\\\\2x-2x=0\\\\0=0\qquad TRUE\\\\Answer:\ \text{Infinitely many solutions}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=\dfrac{3}{2}x+3\end{array}\Rightarrow\left(x,\ \dfrac{2}{3}x+3\right)\right$