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

for part 1. the system has only one solution if the slopes are different.

Answer 2

so an example would be
\[ \large y=2x+1 \]
\[ \large y=3x+1 \]

Answer 3

part 2:

y = 2x + 1

y = 2x + 3

these have the same slope so are parallel and will never intersect

so , no solution

Answer 4

whats part 3 and 1

Answer 5

@cwrw238

Answer 6

for part 1 the lines will intersect and thats 1 solution

Answer 7

part 3

y = 2x + 1

2y = 4x + 2

the second equation = first x 2

and is really the same line

if you graph them you'll get 1 line ( one 'on top' of the other) so you can say that they intercept at every point on the line - so infinite solutions

Answer 8

Thanks a bunch