I'm going to assume that g and y are the same thing here, on a normal xy-coordinate plane. If there is actually a third dimension, 'g', then I am probably wrong, and I apologize.

For a system of 2 linear equations, a 'solution' is a point of intersection for the two lines.

If the two lines are parallel, they will have no intersection. These two equations are in the form y = mx + b, where m is the slope. If their slopes are the same, then the lines are parallel. The first equation has a slope of 2. The second equation has a slope of 6. 2 ≠ 6, obviously. They are are not parallel, so there is at least one solution (intersection)

If two equations are 'equivalent', then they represent the same exact line and you cannot find a unique solution to the system because there is no single point where they intersect. They intersect at all points, so there are an infinite number of solutions. Two equations in the same format (like point-slope) will be equivalent if you see that one is just a multiple of the other. That is not the case here. They are not equivalent, so there are not an infinite number of solutions.

For the intersection of two lines in a plane, that intersection is no point, 1 point, or infinite points.

We have ruled out no point and we have ruled out infinite points.

There must be a solution of one point where the two lines intersect.

That would be consistent with answers B and E as shown in your Brainly question.

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