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 ======================= 1/2y = -x + 5 2y = -4x + 20 y = -2x + 10 y = -2x + 10
same equation.....same line...infinite solutions...EQUIVALENT =================== y = -x + 4 x = -y - 6 y = -x - 6
same slope, different y intercepts....parallel lines......no solutions...this means INCONSISTENT ================== y = 4x + 2 y = 6x - 10 different slopes, different y intercepts...one solution...CONSISTENT ================== y = 2x + 1 y = -2x + 3 different slopes, different y intercepts...one solution...CONSISTENT ================= -2x + 5y = 0 y = 2/5x 5y = 2x y = 2/5x same line....infinite solutions....EQUIVALENT
