Question

$2x + 3y = 5 \\ 3x - 2 = 12 \: \: \\ \\ \\ \\ answe r \: it \: intelligent$
​

Answer 1

Answer:

x = 14/3 , y= - 13/9

Step-by-step explanation:

2x + 3y = 5

3x - 2 = 12

3x = 14

x = 14/3

28/3 + 3y = 5

28/3 + 3y = 15/3

3y = - 13/3

= - 13/9

Answer 2

Answer:

$\huge\boxed{x=\dfrac{46}{13},\ y=-\dfrac{9}{13}}$

Step-by-step explanation:

You lost the "y" in the second equation.

$\left\{\begin{array}{ccc}2x+3y=5&|\text{multiply both sides by 2}\\3x-2y=12&|\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+6y=10\\9x-6y=36\end{array}\right}\qquad|\text{add all sides of the equations}\\.\qquad13x=46\qquad|\text{divide both sides by 13}\\.\qquad\boxed{x=\dfrac{46}{13}}$

Substitute it to the first equation:

$2\cdot\dfrac{46}{13}+3y=5\\\\\dfrac{92}{13}+3y=5\qquad|\text{subtract}\ \dfrac{92}{13}\ \text{from both sides}\\\\3y=5-\dfrac{92}{13}\\\\3y=\dfrac{5\cdot13}{13}-\dfrac{92}{13}\\\\3y=\dfrac{65}{13}-\dfrac{92}{13}\\\\3y=-\dfrac{27}{13}\qquad|\text{divide both sides by 3}\\\\\boxed{y=-\dfrac{9}{13}}$