Question

Solve using elimination 2x+3y=12 -4x-6y=-24

Answer 1

$\left\{\begin{array}{ccc}2x+3y=12&|\text{multiply both sides by 2}\\-4x-6y=-24\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+6y=24\\-4x-6y=-24\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=0\qquad TRUE\\\\2x+3y=12\qquad\text{subtract 2x from both sides}\\\\3y=12-2x\qquad\text{divide both sides by 3}\\\\y=4-\dfrac{2}{3}x\\\\Answer:\ \text{It's the dependent system of equations}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=4-\dfrac{2}{3}x\end{array}\right$