Reasoning If the graphs of two linear equations in a system do not intersect each other, what does that tell you about the solution of the system? Explain.
If the graphs of two linear equations in a system do not intersect each other, it tells us that there is no solution to the system.
This is because the intersecting point of two linear equations represents the solution to the system. If the graphs do not intersect, it means that there is no point that satisfies both equations simultaneously. In other words, there is no common solution to the system.
Mathematically, if we have two linear equations in the form of y = mx + b, where m represents the slope and b represents the y-intercept, the non-intersecting graphs indicate that the slopes are either equal or the lines are parallel. In the case of equal slopes, the y-intercepts must be different, leading to lines that are distinct and will never intersect. In the case of parallel lines, both the slopes and the y-intercepts will be different, resulting in lines that will never intersect.
Therefore, if the graphs of two linear equations do not intersect, the system is said to be inconsistent, and there is no solution that satisfies both equations simultaneously.