Question

if 2 lines never intersect, how many solutions does the system have?
(the image has four colored boxes with text: \infinite solutions\,
o solution\, \one solution\,
one of these\ (note: likely a typo, maybe
one of these\ or other intended text, but the main question is about the number of solutions for a system of two non - intersecting lines))

Explanation:

To determine the number of solutions for a system of linear equations when the lines never intersect, we use the concept of parallel lines in a system of linear equations (in two variables, typically in the form \(y = mx + b\) where \(m\) is the slope and \(b\) is the y - intercept).

Step 1: Recall the condition for no intersection

For two lines in a plane (represented by linear equations), if they never intersect, they are parallel. Parallel lines have the same slope (\(m_1=m_2\)) and different y - intercepts (\(b_1
eq b_2\)).

Step 2: Relate to the number of solutions

A solution to a system of linear equations represents the point of intersection of the lines. If the lines are parallel (never intersect), there are no values of \(x\) and \(y\) that satisfy both equations simultaneously. So, the system of equations has no solution.

Answer:

The system has no solution. If we consider the options (assuming the options are "Infinite Solutions", "No Solution", "One Solution", "None of These"), the correct option is "No Solution".