Classnotes Systems by Linear Combination 2-23/2-24
Algebra II CP
The 3rd and last method for solving systems of 2 equations in 2 variables is called Linear Combination.
This method will work for all systems, and is less work than substitution.
The goal of Linear Combination is to get either the x variable or the y variable to cancel out. In order for this to happen,
you must leave your 2 equations in standard form and stacked over one another. Examine the coefficients of the terms
and decide if x or y will eliminate from the original system OR if x or y will eliminate if you multiply one equation by a
factor to force the terms to be equal opposites. Once this is in place, “add” the other columns of variables and
constants – thus solving for one of your two variables.
Example: x + 5y = 33
4x + 3y = 13
Notice that neither the x column nor the y column will eliminate if you add straight down
the columns as they are currently written. If however, you multiply the top equation by
-4, the x column would then eliminate. Thus, the new system would look like:
now, “add” each column
-4x -20y = -132
4x + 3y = 13
-17y = -119
y=7
now solve for the value of the y-coordinate
It is your choice as to which of the original equations you substitute the value y = 7 into to get the value for x. I am going
to use the 1st equation: x + 5(7) = 33
x + 35 = 33 subtract 35 from both sides
x = -2
Therefore the ordered pair solution for this system is ( -2, 7)
There are more examples in your textbook in section 3.2
Classwork for the day is p. 152 #23-34
I have tentatively set the chapter 3 test for next Wednesday, March 2