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

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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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