I didn’t get as much work done this week as I had hoped. I started the week working on the Unit Systems of Equations where I learned that two related equations equal a “System of Equations” (ex. 5f + 10t = 5500 and f + t = 900) and how to solve for the point at which they intersect on a graph. The two methods I learned for solving a system of equations are the:

• Elimination Method
  • To use this method, you manipulate one equation so that it has a variable of equal absolute value to the other equation BUT it is the positive/negative opposite of the other equations variable. You then add the equations together and, since the variables with equal absolute value have opposite signs, they cancel out.
    • Ex. (2y + 7x = -5), (5y – 7x = 12)
  •   In the example above, the +7x and -7x cancel out leaving (2y = -5) and (5y = 12).
    • 2y + 5y = -5 + 12 —> 7y = 7 —> y = 1
  • It is called the Elimination method because you eliminate one variable in order to solve for the other. In this example it wax x.
• Substitution Method
  • This method can be used when you have one equation which tells you exactly what one variable equals, even if it does so by using the other variable.
    • Ex. (3x + y = -3) and (x = -y + 3)
  • In the above example, you can substitute -y + 3 into the 1^st equation in the place of x.
    • 3x + y = -3 —> 3(-y + 3) + y = -3 —> -3y + 9 + y = -3 —> -2y + 9 = -3 —> -2y = -12 —> y = 6

I also learned that:

1. When a system of equations intersects at exactly one point it has one solution and it is referred to as “independent” and “consistent”,
2. When a system of equations has two equations that are exactly the same it has infinite solutions and is referred to as “dependent” and “consistent”, and
3. When two lines in a system of equations are parallel and not on top of each other, there are no solutions and it is referred to as “inconsistent”.

I finished both Systems of Equations and the following unit Expressions with Exponents, although the latter was ~90% finished before I started. I hadn’t worked with exponents since Week 3 and it was a good refresher of how and when to add, subtract, multiply, and divide exponents. It was frustrating at first not remembering how to do it but I was pleasantly surprised at how quickly it all came back to me.

As I said at the start, last week I hoped to be further along at this point than I am. I thought I’d manage to get started on the upcoming unit Quadratics and Polynomials. This unit looks fairly large and, unlike at the start of some other units, nothing has been completed ahead of time. My plan is to force myself to finish this unit this coming week and then finish the remaining unit of the Algebraic Basics course in Week 8 (Equations and Geometry). Can someone tell me what the hell a quadratic is?