Question

PLEASE HELP I WILL FAN AND GIVE MEDAL!!!

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

hmmm i think
An equation in slope intersect form is the equation of a line, or a linear equation. When you have two linear equations, they may represent 2 lines that intersect at one point. Then you have one solution. They may also represent parallel lines. Then they don't intersect, and there is no solution. Finally they may represent only one single equation. Then you have an infinite number of solutions.

a. y = 5x + 6
y = -2x + 3
These lines have different slopes, so they must intersect at one single point. There is one solution.
b. y = 2x + 6
y = 2x -2
These lines have the same slope, so they don't intersect. They are parallel. In addition, since they have different y-intercepts, they are clearly two different lines. There is no solution.
c. y = 2x + 6
y = 2x + 6
These two equations have the same slope and the same y-intercept. They represent one single line, so there are infinitely many solutions.