Question

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.

Answer 1

True:
- The system has one solution. (The lines have different slopes, so they meet once.)
- Both lines have the same y-intercept. (Both simplify to y = (1/2)x + 5 and y = x + 5, so both b = 5.)
- The solution is the intersection of the 2 lines. (Their intersection point is (0, 5).)

False:
- The system graphs parallel lines. (Slopes 1/2 and 1 are different.)
- Both lines have the same slope. (Slopes are 1/2 and 1.)
- The equations graph the same line. (Different slopes, so different lines.)