Two days ago I thought I’d be starting this post by saying “Systems of Equations are F-ing hard”. Writing this now, I still think they can be tricky, but I’m happy to say I just passed the unit test of System of Equations with a 100% score on my first try! What’s even better is that’s the second unit test I passed this week with 100% score. 🙂
The first unit I went through this week was Forms of Linear Equations. This was once again a “refresher” unit for me having worked on these types of questions in weeks past. The unit brought me back to working with linear equations on graphs and understanding their formulas. This unit highlighted three forms of liner equations; Point Slope Form, Slope Intercept Form, and Standard Form. The pros and cons of each form are:
- Point Slope Form: (y – b) = m(x – a)
- Easy to determine slope
- Difficult to determine X- and Y-intercepts
- Slope Intercept Form: y = mx + b
- Easy to determine slope and Y-Intercept
- Difficult to determine X-intercept
- Standard Form: Ax + By = C
- Easy to determine X- and Y-intercepts
- Difficult to determine slope
The second unit, Systems of Equations, got me back into solving a (you guessed it) system of equations to determine its solution (i.e. the point(s) at which the two lines intersect on a graph, if at all). One thing that I got a better understanding of this week is when a SoE has one solution, no solution or infinite solutions. In summary:
- If the two lines in a SoE intersect at one point, they have one solution,
- If the two lines in a SoE have the same equation, there are infinite solutions, and
- If the lines in a SoE don’t intersect, they have no solutions.
Another thing that started to make much more sense to me after completing this unit was the Elimination Method. This is a method used to solve for one variable (ex. y) in a SoE by eliminating the other variable (ex. x) by manipulating one equation to have the same absolute value of one variable as the other equation and then either adding or subtracting the two equations to get rid of that variable. Examples:
- 8x + 2y =
12 and -4x + 3y = 7 —> 8x + 2y = 12 and 2(-4x + 3y) = 2(7) —> 8x
+ 2y = 12 and –8x + 6y = 14 —>
ADD TWO EQUATIONS —>
8x + (-8x)+ 2y + 6y = 12 + 14 —> 8y = 26 —> y = 26/8
- 5x + 4y =
6 and 10x + 6y = 14 —> 2(5x + 4y) = 2(6) and 10x + 6y = 14 —> 10x
+ 8y = 12 and 10x + 6y = 14 —>
SUNTRACT TWO EQUATIONS —>
10x – 10x+ 8y + 6y = 12 + 14 —> 14y = 26 —> y = 26/14
The part of the Elimination Method that confused me the last time was determining when to add and when to subtract the two equations. It seems very obvious to me now that when the two variables of equal absolute values have the same sign (i.e. either + or -) you subtract them and when they have the opposite signs you add them.
I haven’t mentioned before that each unit in KA has a certain number of “Mastery Points” (MP) which in a way indicate how big a unit is (for example, the last unit, System of Equations, had 1400 MP). When I watch videos, work through practice questions, and finish the unit test, KA gives me MP towards the unit. All that to say, the next two units coming up are Inequalities (Systems & Graphs) which has 800 MP and Functions which has 2200 MP. My goal is to get through Inequalities (Systems & Graphs) by Wednesday to give myself a shot at finishing Functions by the end of Week 12. I apologize in advance for the terrible puns I will be using in Week 11 and 12’s posts regarding FUN-ctions.