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Consider the system of linear equations.

2y = x + 10

3y = 3x + 15

Which statements about the system are true? Check all that apply.

The system has one solution.
The system graphs parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations graph the same line.
The solution is the intersection of the 2 lines.

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Hey
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The Best Answer Is - 1. The system does has one solution.
2. The systems doesn't graph as parallel lines.
3. Both lines do not  have a same slope.
4. Both lines do have a y - intercept.
5. The equations don't graph as a same line.
6. The solution is the intersections of two lines.

2y = x + 10
 2         2
 y = 0.5x + 5

3y = 3x + 15
 3          3
  y = x + 5

  0.5x + 5 = x + 5
- 0.5x   - 0.5x
             5 = 0.5x + 5
           - 5             - 5
             0 = 0.5x           0.5    0.5
             0 = x
             y = x + 5
             y = 0 + 5
             y = 5
       (x, y) = (0, 5)

HOPE THIS HELPS!!!
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If I get it WRONG i'm SORRY!!!
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facundo3141592

We want to analyze the given system and see which statements apply to it.

The statements that apply are:

  • The system has one solution.
  • Both lines have the same y-intercept.
  • The solution is the intersection of the 2 lines.

The system is:

2y = x + 10

3y = 3x + 15

Completely isolating y, we get:

y = (1/2)*x + 5

y = x + 5

We can see that both equations have different slopes, thus these lines are not parallel, then the lines intersect at some point, meaning that this system has a unique solution.

We also can see that both lines have the same y-intercept, then we can know that the lines will intercept at that point, meaning that the solution is (0, 5).

Then the statements that apply are:

  • The system has one solution.
  • Both lines have the same y-intercept.
  • The solution is the intersection of the 2 lines.

Where the last statement applies for all systems of linear equations.

If you want to learn more, you can read:

https://brainly.com/question/12895249