Question

2.) How many solutions does the system have

y = 2x -5
y = 2x + 3
3.) How man solutions does the system have?
y = 4/5x + 1
y = -1/2x - 1

Answer 1

Part 1) The system has no solution

Par 2) The system has one solution

Explanation:

Part 1) we have

`y=2x-5` ----> equation A

`y=2x+3` ----> equation B

Remember that

If two lines are parallel then their slopes are equal

In this problem line A and line B have the same slope and different y-intercept

so

The lines don't intersect (the solution is the intersection point both lines)

therefore

The system has no solution

see the attached figure N 1 to better understand the problem

Part 2) we have

`y=(4)/(5)x+1` -----> equation A

`y=-(1)/(2)x-1` -----> equation B

Remember that

If two lines have different slope then the lines have one intersection point

In this problem line A and line B have different slopes

`(4)/(5) \\eq-(1)/(2)`

therefore

The system has one solution (the solution is the intersection point both lines)

see the attached figure N 2 to better understand the problem