(1.2: Solving linear equations) Consider the following linear system with a and b unknown non-zero constants. x1 3x2 + x3 = 4 2x1 8x3 = 2 6x1 + 6x2 + ax3 = b (a) For what values of a and b does the system have in nitely many solutions? (b) Given an example of a and b where the system has exactly one solution. (c) Give an example of a and b for which the system has no solutions.

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?