What will the graph look like for a system of equations that has no solution? (1 point)
A. You will see the lines intersect at only one point.
B. You will see perpendicular lines.
C. You will see lines on top of each other so that they form the same exact line.
D. You will see parallel lines.
E. You will see the lines intersect at two different points.
D. You will see parallel lines.
D. You will see parallel lines.
The correct answer is D. You will see parallel lines.
To understand why the graph of a system of equations with no solution consists of parallel lines, we need to consider the nature of the equations themselves.
A system of equations is a set of equations with multiple variables. In this case, we are considering a system of linear equations with two variables, typically represented by x and y. Each equation in the system represents a line on the coordinate plane.
When solving a system of linear equations, the solution represents the point(s) of intersection between these lines. If the lines intersect at a single point, we have a unique solution. If the lines intersect at multiple points, we have infinitely many solutions. However, if the lines are parallel, they will never intersect, and therefore the system of equations has no solution.
Visually, this means that the graph of a system of equations with no solution will consist of two lines that are always equidistant from each other and will never intersect, forming parallel lines.
Therefore, the correct choice is D. You will see parallel lines when the system of equations has no solution.