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

User Stian Svedenborg
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2.7k points

2 Answers

17 votes
17 votes

Answer:

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.

User Gilberto Ibarra
by
2.4k points
9 votes
9 votes

Answer:

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

User Lazloo Xp
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3.0k points