Answer:
To graph the system of equations and find the solution, follow these steps:
1. Graphing the system of equations:
- Convert each equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
- For the equation y = 3x + 9, the slope is 3 and the y-intercept is 9. Plot a point on the y-axis at (0, 9) and use the slope to find additional points on the line.
- For the equation 6x - 2y = 6, rearrange it to the slope-intercept form: y = 3x - 3. The slope is 3 and the y-intercept is -3. Plot a point on the y-axis at (0, -3) and use the slope to find additional points on the line.
- Graph the two lines on the same coordinate plane.
2. Finding the solution to the system:
- Determine the point(s) where the two lines intersect on the graph.
- If the lines intersect at a single point, there is one unique solution to the system.
- If the lines are parallel and do not intersect, there is no solution.
- If the lines coincide and overlap each other, there are infinitely many solutions.
Based on the graph, we can determine the solution to the system of equations:
- Looking at the graph, the two lines intersect at the point (0, -3).
- Therefore, the solution to the system of equations is (0, -3).
The correct answer choice is C. There is one unique solution (0, -3).
Explanation: