Which of the following systems of equations has no solution?
1. { y = 8x - 17 \ y = -8x + 17 }
2. { y = (2/3)x - 3 \ y = (2/3)x + 4 }
3. { y = 2x - 5 \ 2y = 4x - 10 }
4. { y = 3x + 4 \ y = -(1/3)x + 4 }
The system y = 8x - 17 and y = -8x + 17 has a solution because the lines intersect.
The system y = (2/3)x - 3 and y = (2/3)x + 4 has no solution because the lines are parallel and have different y-intercepts.
The system y = 2x - 5 and 2y = 4x - 10 has infinitely many solutions because the equations are equivalent.
The system y = 3x + 4 and y = -(1/3)x + 4 has a solution because the lines intersect.
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