Let's start with first equation
We need to bring both equations in the form y = mx + b
2x + 3y = 7 (original equation)
-2x -2x (subtract 2x from both sides)
________________
3y = -2x + 7
(3y/3) = (-2x + 7)/3 (divide both sides by 3)
y = (-2/3)x + 7/3 --------------(1)
Let's do the second equation
4x + 6y = 11 (original equation)
-4x -4x (subtract 4x from both sides)
____________
6y = -4x + 11
(6y/6) = (-4x + 11)/6 (divide both sides by 6)
y = (-4/6)x + 11/6
or y = (-2/3)x + 11/6 --------------------(2)
As, you can see slopes in both equations (1) and (2) are same. That's why these lines are parallel.
