Question

Based on the graph of the following system of equations, determine number of solutions.
2x + 3y = 9
6y = 5 - 4x

Answer 1

Well I don't have the graph, but you can determine the number of solutions without it.

You can do so a couple different ways.

To start of, let us call 2x + 3y = 9 (1), and 4x + 6y = 5 (2). Notice I rearranged (2).
We can use elimination to solve for one variable. Multiply the first equation by -2, because we want to cancel a variable. BUT LOOK WHAT HAPPENS.

If you add:
-4x - 6y = -9
4x + 6y = 5
-------------
0 = -4

That is obviously not true. This means the lines do not intersect, and are parallel. THERE ARE NO POINTS OF INTERSECTION. No solutions.

Answer 2

And now I see the graph and that confirms it!

Answer 3

no solutions, note that the ratios of the coefficients are the same, that means the slope is the same 2:3 4:6

Answer 4

So the graph illustrates they are parallel and therefore can't intersect anywhere. If the problem is looking for an algebraic confirmation, all you have to do is try to solve it like any other system of equations, and then it quickly becomes apparent that there are no solutions! :) Hope this helped