Question

Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.

Answer 1

There is no solution, since the lines are parallel.

Explanation:

The first thing to do is change each equation to slope intercept form. Slope intercept form: y = mx + b.

2x - 3y = -6 in slope intercept form is y = 2/3x + 2 (subtract 2x from both sides, then divide both sides by -3). -3y + 2x = 3 in slope intercept form is y = 2/3x - 1 (subtract 2x from both sides, then divide by -3).

The slope of both these equations are the same: 2/3. Since these lines have the same slope but different y-intercepts, they are parallel, which means they will never cross, so there's no solution.

Hope this helps!