Can someone please help. Explain how you can determine from the graph of a system of two linear equations in two variables whether it is an inconsistent system of equations. Thanks
Parallel lines never cross. If you see parallel lines, then this is an inconsistent system of equations.
Certainly! To determine whether a system of two linear equations in two variables is inconsistent, you can analyze its graph. Here's how you can do it:
Step 1: Graph the two equations on the coordinate plane. To do this, you can convert the equations to slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. This form makes it easier to identify the slope and y-intercept values.
Step 2: Once you have the equations in slope-intercept form, plot the lines on the graph. It's important to plot both lines accurately.
Step 3: Analyze the graph. There are three scenarios you may encounter:
1. Intersecting Lines: If the two lines intersect at a single point, then the system of equations has a unique solution. This means that there is one specific value for both variables that satisfies both equations simultaneously.
2. Parallel Lines: If the two lines are parallel and do not intersect, then the system of equations has no solution. This signifies an inconsistent system. Parallel lines have identical slopes but different y-intercepts, which prevent them from intersecting.
3. Overlapping Lines: If the two lines coincide and overlap each other, then the system of equations has infinitely many solutions. This indicates a consistent system. Overlapping lines have the same slope and the same y-intercept.
By visually analyzing the graph, you can identify whether a system of linear equations is inconsistent or consistent with a unique or infinite solution.