Answer:
Part 1) we have
----> equation A
Isolate the variable y
----> equation B
Compare the slope of both lines
The slopes are different
That means
The lines intersect at one point
therefore
The system has one solution
Part 2) we have
isolate the variable y
-----> equation A
isolate the variable y
----> equation B
Compare equation A and equation B
The slopes are equal
The y-intercept are different
That means
we have parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
Part 3) we have
isolate the variable y
-----> equation A
isolate the variable y
----> equation B
Compare equation A and equation B
The equations are identical
That means
Is the same line
so
The system has infinitely solutions
Part 4) we have
isolate the variable y
-----> equation A
isolate the variable y
----> equation B
Compare the slope of both lines
The slopes are different
That means
The lines intersect at one point
therefore
The system has one solution
Part 5) we have
isolate the variable y
-----> equation A
isolate the variable y
----> equation B
Compare the slope of both lines
The slopes are different
That means
The lines intersect at one point
therefore
The system has one solution
Part 6) we have
isolate the variable y
-----> equation A
isolate the variable y
----> equation B
Compare equation A and equation B
The slopes are equal
The y-intercept are different
That means
we have parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
Step-by-step explanation:
