consistent means 1 solution
inconsistent means no solutions....because they are parallel lines
equivalent means infinite solutions...because they are the same line
y = 3x - 2 3x - y = 4
-y = -3x + 4
y = 3x - 4
both equations have the same slope but different y intercepts....this means they are parallel lines and have no solutions ....INCONSISTENT
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1/2y = -x + 5 2y = -4x + 20
y = -2x + 10 y = -2x + 10
same equation.....same line...infinite solutions...EQUIVALENT
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y = -x + 4 x = -y - 6
y = -x - 6
same slope, different y intercepts....parallel lines......no solutions...this means INCONSISTENT
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y = 4x + 2 y = 6x - 10
different slopes, different y intercepts...one solution...CONSISTENT
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y = 2x + 1 y = -2x + 3
different slopes, different y intercepts...one solution...CONSISTENT
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-2x + 5y = 0 y = 2/5x
5y = 2x
y = 2/5x
same line....infinite solutions....EQUIVALENT