Simultaneous equations (Same equation) I was thinking of a 'stupid question' this morning.
How many solutions do these simultaneous equations have?
$$4x+3y = 3$$
$$6y-6 = -8x$$
Basically they are the same equation. But should I say they have infinite solutions or? What's the correct term should I use?
 A: They are not the same equation, but they are equivalent statements. That means that if the first one is true, so is the second, and vice versa. The number of solutions to the system is then the number of solutions to either of the individual equations.
In this case, assuming $x$ and $y$ are meant to be real numbers, then we can see that there are an infinite number of solutions. Indeed, if $x^*$ is some value for $x$, then we can choose $y^* = 1 - \frac{4}{3}x^*$ for $y$, in order to have equality. Since we can do this for any $x^*$, and there are an infinite number of choices (all real numbers), there is an infinite number of solutions.
Note that the number of solutions may be different if you are only interested in rational or integer solutions to the system, but in any case, these are equivalent statements. 
A: Yes, they have infinitely many solutions; any point satisfying one (of which there are infinitely many) must satisfy both.
A: Draw the curves, note that those two straight lines are same (coincides actually). So, you have infinitely many solutions.
