Question

which statement is true about the system of linear equations graphed in the coordinate plane below?
it has one solution at (4, 1).
it has no solution.
it has one solution at (1, 4).
it has infinitely many solutions.

Explanation:

Step1: Analyze the lines' slopes

The two lines in the graph are parallel (same slope, different y - intercepts). For a system of linear equations \(y = m_1x + b_1\) and \(y=m_2x + b_2\), if \(m_1=m_2\) and \(b_1
eq b_2\), the lines are parallel and never intersect.

Step2: Determine the number of solutions

A solution to a system of linear equations is a point \((x,y)\) that lies on both lines. Since parallel lines never intersect, there is no point that lies on both lines. So the system has no solution.

Answer:

It has no solution.