solving a system of linear equations that is inconsistent or consistent dependent

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I am working on inconsistent and consistent does this problem have a solution, infinite or unique if so what are they.. x-3y+3=0

                                           -x+3y=3

Jun 16th, 2015

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x - 3y + 3 = 0 ---(1)

-x + 3y = 3 ---(2)


Subtracting 3 from both sides of equation (1), we get

x - 3y + 3 - 3 = 0 - 3

x - 3y = -3 ---(3)


Multiply both sides of equation (2) by -1

-1(-x + 3y) = -1*3

x - 3y = -3 ---(4)


Equations (3) and (4) are same. So, equations (1) and (2) represent the same line.

Hence, every point on the line is a solution to the equation and there are infinite such points.

Therefore, the system of equations is consistent and has infinite solutions.

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Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 16th, 2015

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