A system of linear equations can have zero, one, or an infinite number of solutions.

Question

a) Describe a rule that can be used to determine the number of solutions a system of linear equations will have.

b) use the base example of two people walking to describe a system of two linear equations that has

I. 0 solutions:

II. 1solution:

III. An infinite number of solutions

Answer 1

a)

If two equations have the same slope, but different y intercept, there is zero solutions

same m, different b, then zero solutions. y=mx+b, m=slope, y= intercept

if two equations have the same slope but the same y intercept, there are infinite solutions

same m, same b, then infinite solutions

if two equations have different slopes, there is one solution, m1 doesn't = m2, then one unique solution, and that's regarfless of the b value

b)

If 2 people walk at the same speed, they never meet, with zero solutions. Unless they start at the same time then there's infinite solutions.

If they have different speeds, they intersect at one point and there's one unique solution.