Problems for Day 1

Types of solutions

Here are a few quick problems for you to think about. Don’t forget that there’s also one MyOpenMath problem for you to do for actual credit! Problem #3 on this sheet is a lot like that.

1. Activity 1.3 part (a) from our text

2. Activity 1.3 part (b) from our text

3. Consider the system \[ \begin{aligned} 2x+3y&=3 \\ ax+y&=c. \end{aligned} \] Find values of \(a\) and \(c\) such that

   1. The system has exactly one solution
   2. The system has infinitely many solutions
   3. The system has no solutions.

   Be sure to think geometrically - it might even help to draw a graph!

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