solving system graphically

Question

solve each system graphically, check solution and if solution has infinate solutions use set-builder notation to write the solution set

2x-3y=6,

3y-2x=-6

Answer 1

2x - 3y = 6

3y = 2x - 6

y = (2/3)x - 2

.

3y - 2x = -6

3y = 2x - 6

y = (2/3)x - 2

.

Note:  We'll still graph it, but we don't need to because the equations are identical, which means infinite solutions.

Graphed on graphsketch.com:  http://graphsketch.com/?eqn1_color=1&eqn1_eqn=(2%2F3)x%20-%202&eqn2_color=2&eqn2_eqn=&eqn3_color=3&eqn3_eqn=&eqn4_color=4&eqn4_eqn=&eqn5_color=5&eqn5_eqn=&eqn6_color=6&eqn6_eqn=&x_min=-10&x_max=10&y_min=-10&y_max=10&x_tick=1&y_tick=1&x_label_freq=5&y_label_freq=5&do_grid=0&do_grid=1&bold_labeled_lines=0&bold_labeled_lines=1&line_width=4&image_w=850&image_h=525

There's only one line on the graph because the two lines are the same.

Answer:  { (x,y) | 2x - 3y = 6 }