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Graph the following system of equations.

y = 3x + 9
6x − 2y = 6

What is the solution to the system?

A.There is no solution.
B.There is one unique solution (−1, −6).
C.There is one unique solution (0, −3).
D.There are infinitely many solutions

1 Answer

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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:

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