Question

Hi,
I have a question about systems of equations. Here's my problem: "How many solutions are there to this system of equations?" The equations: 3x+5y=-2; 6x=4-10y

The equations ARE different when you solve them. Here's what my question is. When you have 2 equations that are different, how many solutions are there?

Thanks so much! :)

Answer 1

No solution. Suppose we number the equations (1) and (2). Rearrange (2) to become (2)* which is 3x+5y=2. Subtract (1) and (2)* to get 0=-4, which is a contradiction. This contradiction shows us that this system is inconsistent, and has no solution.

Answer 2

You could put both equations into slope intercept form and plot them. The solution is where they cross (intersect). That one point satisfies (lies on both) lines.

Of course things can go wrong: if the lines are parallel they never cross. That is what you have here.

Another thing that can happen is that both equations turn out to be the same line. So you have an infinite number of solutions. All points on the first line will be on the second line (which is really the first line, if that makes sense).