Question

A coordinate grid with 2 lines. The first line labeled f(x) passes through (negative 3, 3), (0, 2), and (3, 1). The second line labeled g(x) passes through the points at (negative 3, 0) and (0, 2)

What is the solution to the system of linear equations?

Answer 1

Explanation:

the solution of a system of 2 equations (lines or other forms of functions) is the set of all intersection points.

that is where the equations are equal, share the same "behavior".

for 2 lines it is only possible to have

• no intersection point (no solution) - when they are parallel.
• 1 intersection point (1 solution) - normal case.
• infinitely many intersection points or solutions - when they are identical.

in our case here we see that most points are different.

so, the lines are not identical.

and there is one point they have in common : (0, 2).

that is the solution, the one intersection point.

since they have a point in common, they cannot be parallel.