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What will the graph look like for a system of equations that has no solution? (1 point) You will see the lines intersect at only one point. You will see lines on top of each other so that they form the same exact line. You will see the lines intersect at two different points. You will see perpendicular lines. You will see parallel lines.
You will see parallel lines.
When a system of equations has no solution, the graph will show parallel lines.
To determine what the graph of a system of equations with no solution looks like, we need to understand the concept of parallel lines. Two lines are parallel if they have the same slope but different y-intercepts. Parallel lines never intersect, meaning they do not have any common solutions.
Now, when we have a system of equations with no solution, it means that the lines represented by the equations are parallel. Therefore, the correct answer is "You will see parallel lines" as they will not intersect at any point. This is a visual representation of the fact that there is no solution to the system of equations.
To graph the system of equations and confirm that the lines are parallel, you can follow these steps:
1. Convert each equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
2. Plot the y-intercept on the graph for each equation.
3. Use the slope to find a second point on each line by moving up or down (increasing or decreasing y) and right or left (increasing or decreasing x) according to the given slope.
4. Connect the two points for each line using a straight line.
5. If the lines are parallel, they will never intersect, and you will see two distinct lines that do not overlap or cross each other.
By following these steps, you will be able to understand and visually confirm that a system of equations with no solution results in parallel lines on the graph.