## Wednesday, February 16, 2011

### Solving Systems of Equations (graphing, substitution, elimination/addition)

The reason for solving systems of equations is to find at which point will they intersect on a graph.
A "system" of equations is 2 equations where the x's in each equation equal the same number, and the y's in each equation equal the same number.
When you find what x and y equal, they are written in parentheses as an ordered pair like this:  (-3, 5) with the x always being written before the y.  If you graph the (-3, 5) -- use the slope-intercept form "rise over run" -- that is where the two graphed equations (lines on the graph) would intersect.

►After graphing, if lines are parallel they will not intersect.  The answer to this kind of problem is "no solution."  There is no point on the graph at which the lines will intersect.

►If the lines end up graphing as the same line, on top of one another, the answer is "infinite solutions" or "entire line."  In other words, ANY of the points on the entire line will work in both of the systems of equations.

►If the lines do intersect, the point at which they intersect is your answer.  You will write the answer as an ordered pair, such as (-2, 5).

A. Solving Systems of Equations by Graphing

(1) Solving Systems by Graphing (YayMath.org - my favorite math videos!)
►Accompanying worksheet for this video.

(2) Solving Systems by Graphing

(3) Solving Systems by Graphing [y-intercept (b) is zero]

B.  Solving Systems of Equations by Substitution

(4) YourTeacher.com - Solving Systems by Substitution

(5) YayMath.org - Solving Systems by Substitution
►Accompanying worksheet for this video (only do the Substitution method problems for now).

C. Solving Systems of Equations by Elimination

(6) YayMath.org - Solving Systems by Elimination/addition.
►Accompanying worksheet for this video.

"To 'eliminate' may make you think of the Terminator. But in Algebra, it's a method of solving two or more equations at the same time."  ~Yay Math!

(7) YayMath.org - Solving Systems by Elimination/addition.
►Accompanying worksheet for this video (use the last problem -- this is the rest of the video from #5 above).  Full video here.