# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent  2x + 3y = 3 and 3x – 2y = 11?

Apr 5, 2017

The system is consistent.

Point of intersection $\to \left(x , y\right) = \left(3 , - 1\right)$

#### Explanation:

Manipulation of these equations gives:

$y = - \frac{2}{3} x + 1$

$y = \frac{3}{2} x - \frac{11}{2}$

The gradients are different and the #y_("intercepts")' are different. Therefore the straight lines to cross.

Thus this is a 'consistent' system of equations (has a solution).

Solution by graph: