Question
What will the graph look like for a system of equations that has no solution?
A You will see the lines intersect at only one point.
B You will see lines on top of each other so that they form the same exact line.
C You will see perpendicular lines.
D You will see parallel lines.
E You will see the lines intersect at two different points.
The correct answer is option D: You will see parallel lines.
When a system of equations has no solution, the lines represented by the equations are parallel and never intersect.
B You will see lines on top of each other so that they form the same exact line.
To determine what the graph of a system of equations with no solution looks like, we need to consider the characteristics of the equations involved.
A system of two linear equations in two variables, such as y = mx + b, represents a set of points on a coordinate plane that satisfy both equations simultaneously. There are three possibilities for the graphical representation of a system of equations:
1. If the lines representing the equations intersect at one point, it means that the system has a unique solution. This occurs when the lines have different slopes and different y-intercepts.
2. If the lines representing the equations are on top of each other, it means that the equations are equivalent. In other words, they represent the same line. This indicates that the system has infinitely many solutions.
3. If the lines representing the equations are parallel, it means that the system has no solution. This occurs when the lines have the same slope but different y-intercepts.
Therefore, the correct answer is D: You will see parallel lines.