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# how many solutions are there for pair of equations y=0 and y=5 and why?explain it

plz explain the solution in brief and show the solutions step wise.

### 2 Answers by Expert Tutors

Kenneth S. | Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018Expert Help in Algebra/Trig/(Pre)calculu...
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y cannot be both 0 and 5 at the same time; these equations contradict each other, so that 'system' has NO solution.
Andrew M. | Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/HonorsMathematics - Algebra a Specialty / F.I....
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y = 0
y = 5

These are both horizontal lines, parallel to each
other.  As such there is no crossing point,
or point in common, thus the system has no
solution.
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Put the lines in slope intercept format:
y = mx + b, m=slope, b = y-intercept.
If the slope is the same they are parallel.
If they are parallel and the y-inercept
is different, the lines never cross.

y = 0
y = 0x + 0
m = 0, b = 0

y = 5
y = 0x + 5
m = 0, b = 5

Same slope, different y-intercept.  No solutions.

The same is immediately true of a vertical line
of form x = n  where n is some number.
This is a vertical line, straight up and down.
If we have two lines, x = a, x = b and
a and b are different the lines never cross.

Understand?