1/7/2014

Today we learned the second method of solving linear equations: Method of Elimination!

Essentially, the method of elimination has 4 steps:

1.obtain an X or Y coefficient that only differ by sign

2. Add the equations to eliminate the variable

3, back substitute by plugging in

4. Check solution:

  1) algebraically by substituting back into the original system

  2) graphically by drawing the graph 

Graphical interpretation of the solutions

1. two identical lines: unlimited, infinite solutions

2. Two intersected lines: one solution

3. Two parallel lines: no solution

One thing to remember: if there is more than one variable, then there is more than one equation.

Example 1. 

       5x+ 3y= 9

       2x-4y= 14

Step 1: 4( 5x+ 3y)=9x4

            3( 2x-4y)=14x3

            20x+12y= 36

            6x-12y= 42

Step 2: 26x= 78

                X= 78/26 =3

Step 3: y= (2x-14)/4= -2

Step 4: check 

Do you understand this method now?

Stretch your mind:

An airplane is flying into a headwind to a 4000 miles away town in 6 hours and 30 minutes, while on the return flight it only takes 6hours. Find out the speed of plane r1 and that of the wind r2.( hint: look at the picture below and think about the equations)