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

Wow, I had to do something just like this, except it was for linear algebra

Answer 2

I won't xD

Answer 3

1)

y = x
y = -x + 2

The lines representing both equations intersect only once on the xy-axis, so there is only one solution.

2)

y = x
y = x + 2

The lines representing both equations are parallel lines since they have the same gradient.
However, they do not intersect each other, so there is no solution.

3)

y = x
2y = 2x

Both equations represent the same line, so every point on the line is a solution.
Since the line is infinitely long, the number of solutions is also infinitely many.