How many solutions does a linear equation in two variables have?

Yes! A single linear equation in two variables has infinitely many solutions because you can choose any value of x and find a corresponding y. For 2x + 3y = 6: if x=0, y=2. If x=3, y=0. If x=6, y=-2. If x=1, y=4/3. Each (x,y) pair is a solution. Geometrically, a linear equation in two variables represents a STRAIGHT LINE. Every point on the line is a solution. A line has infinitely many points, so infinitely many solutions. You need TWO equations (a system) to get a unique solution, because two lines intersect at exactly one point (unless they are parallel or identical).