Systems Of Linear Equations

In this unit it was explained that 2 or more equations that are on the same plane are PARALLEL, INTERSECTING, OR SUPERIMPOSED.
Also the use of 3 solving methods was explained. The 3 being GRAPHING, SUBSTITUTION, AND ELIMINATION.
The graphing method uses the "y=mx+b", "Ax+By+C=0", And the "y-y1=m(x-x1) formulas, and even the use of the graphing calculator.
The substitution method has 3 steps that help you answer the equations.
Step 1 tells you to put line 1and line 2 into equations.
Step 2 tells you to solve.
Step 3 tells you to put you solution into sentance form.

ex: L1: X+Y=-1
L2:X-2Y=8

Step 1: L1: X=(-1+Y)
L2: (-1+Y)+2Y=8
Step 2: (-1+Y)+2Y=8
-1+3Y=8
3Y=9
Y=3
Step 3: Since Y=3, and since X+2Y=8
Than X+2(3)=8
X+6(-6)=8(-6)
X=2
The solution is therefore (2,3).

The 3rd method, elimination, has 6 to follow.
Step 1 tells you to line up the variables, and the coefficients.
Step 2 tells you to choose a variable and solve for it.
Step 3 says to use algebra to multiply or divide the equation by a value to create Sames or Opposites.
Step 4 explains how to either add or subtract the lines.(Sames are subtracted. Opposites are added.)
Step 5 tells you to solve for the remaining variable.
Step 6 tells you to put you solution into sentance form.

ex: L1:5x+y=16(x3)
15x+3y=48
L2: 2x-3y=3
(add)
(17x)/17=51/17
x=3

And since 5x+y=16
5(3)+y=16
15x(-15)+y=16(-15)
y=1
The solution is (3,1).

This unit also explained how to solve word problems using 4 steps, and any method you choose.
Step 1 tells you to make 2 "Let" statements.
Step 2 tells you to make 2 equations using the 2 variables you created in the first step.
Step 3 tells you to do the math by how ever you find easy.
Step 4 tells you to make a statement to summarize your answer.