Question

How many solutions a system of linear equations have if: Questions. 1.the equations have different slopes? 2.the equations have the same slope and different y-intercepts. 3.the equations have the same slope and same y-intercepts. Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution

Answer 1

1. One solution

2. no solution

3. infinite number of solutions.

Explanation:

How many solutions a system of linear equations have if: Questions.

(assuming a system of two equations)

1.the equations have different slopes?

One unique solution, which is at the intersection point.

2.the equations have the same slope and different y-intercepts.

The equations/lines are then parallel but NOT coincident. They will never meet, therefore NO solution.

3.the equations have the same slope and same y-intercepts.

The two lines/equations are in effect coincident. Therefore there is an infinite number of solutions.

Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution

Answer 2

see below

Explanation:

1.the equations have different slopes? They will intersect at one point so one solution

2.the equations have the same slope and different y-intercepts. They are parallel lines with a different y intercept so they will never intersect - no solutions

3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions