is 2y + 3x =6 and 4y =16 - 6x is consistent and independent, consistent and dependent or inconsistent

Question

ii need help please help me.

Answer 1

The system of equations are 2y + 3x = 6 and 4y = 16 - 6x.

Write the equations in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

Then the equations are y = (- 3/2)x + 3 and y = (- 3/2)x + 4.

Slopes of the above lines are equal, i.e , - 3/2 and they have different y - intercepts, i .e 3 and 4.

So, the given lines are parallel lines.

So, there is no solution exists, then the given system is a inconsistent system.