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. You will see the lines intersect at two different points.
D. You will see parallel lines.
The correct answer is D. You will see parallel lines. You will see the lines intersect at two different points.
To understand why this is the case, let's first discuss what it means for a system of equations to have no solution. In a system of equations, each equation represents a line on a graph. When the lines intersect, that point represents a solution to the system of equations. However, if the lines are parallel, they will never intersect, meaning there is no common point of intersection and therefore no solution to the system of equations.
To determine whether the lines are parallel, we can examine their slopes. If the slopes of the lines are equal, they are parallel. If the slopes are different, the lines will intersect at some point. Therefore, if a system of equations has no solution, the lines must be parallel.
To graph a system of equations and determine if it has a solution or not, we can follow these steps:
1. Write down the equations of the system.
2. Solve each equation for y to express the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
3. Graph each equation by plotting the y-intercept and using the slope to find additional points on the line.
4. If the lines of the graph are parallel, they will never intersect and the system of equations has no solution.