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

Step-by-step explanation:

1. The equations have different slopes.

then one real solution

Example:

subtract both sides of the equations

subtract x from both sides

substitute it to the first equation

If the lines have different slopes, they intersect. The intersection coordinates are the solution to this system of equations.

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

then no solutions

Example:

subtract both sides of the equations

It's FALSE

Conclusion: No solutions

If the lines have the same slopes, they are parallel. If they have different y-intercept, they have no common points (no solutions).

infinitely many solutions

Example:

add both sides of the equations

It's TRUE

Conclusion: infinitely many solutions

If the lines have the same slope and the same y-intercepts, then the equations shows the same line. Two overlapping straight lines have infinitely many common points (infinitely many solutions).

a is the right answer

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)