Question

Choose the correct equation type for each system.

Answer 1

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