Question

Provide a system of TWO equations in slope-intercept form, with only one solution. Using complete sentences, explain why this system has one solution.

Part 2: Provide a system of TWO equations in slope-intercept form with no solutions. Using complete sentences, explain why this system has no solutions.

Part 3: Provide a system of TWO equations in slope-intercept form with infinitely many solutions. Using complete sentences, explain why this system has infinitely many solutions

Answer 1

Ahh I like this question.

1. y=x+0
y=-x+0
\[y=x=-x \rightarrow2x=0 \rightarrow x=0\]
2.y=2x+0
y=2x+1
SInce they have the same slope, they will be parallel and will never intersect

3. y=1+0x
y=1+0x
Different than 2. They have the same slope, yes, but the same y-intercept which means they litereally lie on top of eachother. So every point of one line is every opint of the second line and intercept each other an infinite number of times.