Consider the system of linear equations.2y=x+103y=3x+15Which statements about the system are true? Choose three correct answers.ResponsesThe equations graph the same line.The equations graph the same line.The system has one solution.The system has one solution.The solution is the intersection of the 2 lines.The solution is the intersection of the 2 lines.Both lines have the same y-intercept.Both lines have the same y -intercept.Both lines have the same slope.Both lines have the same slope.The system graphs parallel

To answer this question, let's first rewrite the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

The first equation is 2y = x + 10. Divide everything by 2 to get y = 0.5x + 5.

The second equation is 3y = 3x + 15. Divide everything by 3 to get y = x + 5.

Now, let's analyze the statements:

1. The equations graph the same line: This is false. Although they have the same y-intercept, their slopes are different (0.5 vs 1), so they are different lines.

2. The system has one solution: This is true. Since the lines are not parallel and not the same, they will intersect at one point, which is the solution to the system.

3. The solution is the intersection of the 2 lines: This is true. The point where the two lines intersect is the solution to the system of equations.

4. Both lines have the same y-intercept: This is true. Both lines intersect the y-axis at y = 5.

5. Both lines have the same slope: This is false. The slopes of the lines are different (0.5 vs 1).

6. The system graphs parallel lines: This is false. The lines are not parallel as they have different slopes.

So, the three correct statements are: The system has one solution, the solution is the intersection of the 2 lines, and both lines have the same y-intercept.