Question

write a linear equation that has (a) no solutions and (b) infinitely many solutions. Justify your answer

Answer 1

No solution: y=-x+5, y=-x-1

Infinitely many solutions: y=-4x+1, y=-4x+1

Explanation:

No solution: Slopes are the same and y-intercepts are different.

Infinitely many solutions: The slope and y-intercept (everything) is the same.

Answer 2

System with no solution: Try any pair of lines with equal slopes but different y-intercepts, such as:

y = 2x + 1

y = 2x +3

System with infinitely many solutions:

Try a pair of equations where one equation is a multiple of the other, such as:

2x - 3y = 5

10x - 15y = 25