Question

Solve the system of equations 3x-4y=18 -2x-3y=5

Answer 1

$\left\{\begin{array}{ccc}3x-4y=18&/\cdot2\\-2x-3y=5&/\cdot3\end{array}\right\\\\+\left\{\begin{array}{ccc}6x-8y=36\\-6x-9y=15\end{array}\right\\-------------\\.\ \ \ \ \ \ \ -17y=51\ \ \ \ |:(-17)\\.\ \ \ \ \ \ \ \ \ y=-3\\\\3x-4(-3)=18\\3x+12=18\\3x=18-12\\3x=6\ \ \ \ |:3\\x=2\\\\Answer:x=2\ and\ y=-3\to(2;-3)$

Answer 2

$\left \{ {\big{ 3x-4y=18\ /\cdot2} \atop\big {-2x-3y=5\ /\cdot3}} \right.\\\\ \left \{ {\big{ 6x-8y=36} \atop\big {-6x-9y=15}} \right.\\---------\\-17y=51\ /:(-17)\\.\ \ \ \ \ \ y=-3\\\\3x-4y=18\\\Rightarrow\ \ 3x-4\cdot(-3)=18\ \ \ \Rightarrow\ \ 3x+12=18\ \ \ \Rightarrow\ \ 3x=6\ \ \ \Rightarrow\ \ x=2\\\\ \left \{ {\big{ x=2\ \ \ } \atop\big {y=-3}} \right.$