Question

Part 1: 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

What does slope-intercept form LOOK like?

Answer 2

y = mx + b

Answer 3

This is the answer I put. Is it correct?

y=3x–7 This system has only one solution because the lines
y=–2x+3 intersect only one time.

y=5x+13 This system has no solutions because the two lines
y=5x+12 will never intersect.

y=2x+1 This system has infinitely many solutions because
2y=4x+2 the two lines are on the same points.

Answer 4

Quite so.
Except your last line is not in slope-intercept form :3
(It can't be helped; if you put it in slope-intercept form, it'll be exactly y = 2x + 1)

Answer 5

You might want to mention parallelism for the second pair, and the fact that the third pair has two equations that represent exactly the same line.

But other than that, good work :)

Answer 6

Should I change it to y = 2x + 1?

Answer 7

Well, I don't know HOW strict your instructor is about forms, but you and I both know that
2y = 4x + 2
is *not* in slope-intercept form ^_^

Answer 8

Alright, thanks mate.

Answer 9

No problem.