Liner Equations and Systems Unit Summarization

During this unit we learned the following methods in solving linear equations: substitution, elimintaion, and technology using a calculator, graphmatica, or excel. Personally, I am confidnet using the Substitution method over the other two methods. I am least confident using the Graphing method just because I like being able to see my work. I do not have a problem using the Elimination method; but in the case of trying to solve fractions, the substitution method may be more suitable.

Here are some types of solutions to Linear Systems:

1) To solve these equations, use the formula Ax+By=C. So use m=(-A)/B to find the slope of a line and use b=(-C)/B to find the y-intercept.

a) 2x+3y=5
3x-2y=7
- there is one solution for these equations because they have different slopes (m=(-2)/3 and m= 3/2) and the two lines cross.

b) 6x+12y=21
2x+4y= 7
- there is lots or infinitly many solutions to these two lines because they are super improved lines which means they are the same line and have the same slope and intercept.

c) 5x-2y= 12
-10x+4y=6
-there is no solution to these lines because they have the same slope, different intercepts, and parallel lines.

I sometimes have a hard time with these types of questions so this is something I have to work on. But i find, that instead of thinking of solutions, i like to think of them as coordinates. It enables me to understand the concept better.

Word Problems(not so fun)

I think that word problems are one of the toughest concepts to grasp or figure out. But, i find that if you follow 4 steps, you should be able to gather a basic idea and solution for the question.

Step 1: Name and define 2 variable
- remember to use let statements and i find (in some cases) that it helps to draw a pictures

Step 2: Create two equations using variables

Step 3: Solve using the elimination, substitution, or technolgy.

Step 4: Create a statement to summarize your answer

Each step is worth one mark. Even if you use the wrong answer but still follow the same steps, you will get part marks for showing your work.