Final answer:
The system of linear equations given has no solution and is inconsistent since the lines represented by these equations are parallel and never intersect.
Step-by-step explanation:
The student is presenting a pair of linear equations and asking to determine the type of solutions they have. The equations are:
- 2q = 20 + 5r
- 6q - 15r = 12
To determine the type of solutions, we need to analyze these equations. First, we can simplify the second equation by dividing it by 3, giving us:
Comparing this with the first equation, we see that the coefficients of q and r are the same, but the constants are different (20+5r versus 4). This means the lines are parallel and will never intersect. Therefore, the system has no solution and is considered to be inconsistent.