College Algebra (Abridged)

Plotting these points on the graph, gives us we get the infinitely many solutions to this set of equations. The graph is given as follows:

Case III: System of Equations with No Solution 2 – = 1 …………………………………………………..(1) 8 – 4 = 12 ………………………………………………….(2) Solving equation (1) for the value of ,

= 2 – 1 Substituting the value of in equation 2, 8 – 4(2 − 1) = 12 Solving the equation for the value of , 8 – 8 + 4 = 12 4 = 12 This is clearly impossible, hence we can say that the given system of equations has no solution. Plotting both these equations on the graph (using the same basis as in case II), we get the following representation:

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