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3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent System of Equations Two or more equations with the same variables. To solve a system of equations, you must find where the graph of the equations intersect. Consistent vs. Inconsistent Consistent – one or more solution (points where the graph intersect) Inconsistent – No solution (no intersects) Inconsistent have the same slope. Consistent Inconsistent Independent vs. Dependent Independent – One solution (Consistent) Dependent – Many solutions ( the same equation) Dependent y = 3x + 5 -6x + 2y = 10 The same line. So all the order pairs are the same. In a Consistent System there can only be one The answer (order pair) is correct in both equation. 3x – 7y = - 6; -7y = -3x – 6; X + 2y = 11; 2y = - x + 11; 3 6 y x 7 7 1 11 y x 2 2 Then we graph y 3 6 x 7 7 and y 1 11 x 2 2 Then we graph y 3 6 x 7 7 5,3 and y 1 11 x 2 2 There must be a better way The rest of the chapter show a better way. So on to Section 3.2