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

Question

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calculista calculista · Answer 1 · 2020-01-19T13:30:51+01:00

Answer:

Part 1) The system has no solution

Par 2) The system has one solution

Step-by-step explanation:

Part 1) we have

[tex]y=2x-5[/tex] ----> equation A

[tex]y=2x+3[/tex] ----> 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

[tex]y=\frac{4}{5}x+1[/tex] -----> equation A

[tex]y=-\frac{1}{2}x-1[/tex] -----> 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

[tex]\frac{4}{5} \neq-\frac{1}{2}[/tex]

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