Warm Up:  1) Name the three parent functions and graph them.  2) What is a system of equations? Give an example.  3) What is the solution to a system of equations?

 What is a system of equations?  What is the goal?  A system of equations is a set of two or more equations that may be plotted on the same coordinate system.  The goal in solving is to see where the equations intersect or have the same ordered pair, (x, y).

 What happens if the two lines never touch/ cross?  What happens if, when both lines are graphed, and I only see one line?  This means the lines are parallel (have the same slope) and have no solution, since the solution is the place they cross and this never happens.  This means one equation simplified to the other one, so they are the same line. They have INFINITELY MANY solutions.

Aim #2.2: How do we solve systems of equations by substitution?  What is a substitution?  Substitution means replacing one thing with another, like a substitute teacher. This method is a more algebraic way to solve a system of equations.

Aim #2.2: How do we solve systems of equations by substitution?  How do we solve by substitution?  One of the equations needs to be solved so that either x or y is alone. Check to see if this is already done. If not, you will need to pick one equation and do this.  Substitute that equation into the other equation for that variable.  Simplify and solve for the remaining variable. This should result in x or y equal to a numerical answer.  Take the answer you found and substitute it back into one of the original equations and solve for the remaining variable.  Take both answers and write as an ordered pair. This is your solution.

Aim #2.2: How do we solve systems of equations by substitution?  Reminder:  If you get 0=0, 2x=2x or any true statement …  If you get an UNTRUE statement  (like 5 = 3, or -2 = 9 ),  Then you have INFINITELY MANY solutions.  Then then the lines will never cross and there is NO SOLUTION.

Aim #2.2: How do we solve systems of equations by substitution?  Practice: a) x + y = 9 2y – 7x = 26 c) 3x – y = 5 6x – 5 = 2y b) 3x = 5 – y 6x + 2y = 10

Aim #2.3: How do we solve systems of equations by elimination?  Let’s review the ways to solve systems:  1. Graphing  2. Substitution method  3. Elimination method  What is elimination?  When we eliminate something, we get rid of it or make it equal to zero. So, our goal using this method is to make sure when we add our equations together, one of the variables will add to zero so we can solve for the remaining variable.

Aim #2.3: How do we solve systems of equations by elimination? 6x – 3y = 3 -6x + 5y = 3

Aim #2.3: How do we solve systems of equations by elimination?  What are the steps to solving by elimination?  Make sure both equations line up, x is over x, y is over y, equal sign is over equal sign, and constant is over constant.  Check if one of the variables has opposite coefficients (one is positive and one is negative, both the same number). If not, decide what to multiply one or both by so they have the same but opposite numbers.  Add the two equations together. One of your variables should add to zero.  Solve for the remaining variable.  Write the two answers you found in ordered pair form (x, y).

Aim #2.3: How do we solve systems of equations by elimination?  Remember:  If you get 0=0, 2x=2x or any true statement …  If you get an UNTRUE statement  (like 5 = 3, or -2 = 9 ),  Then you have INFINITELY MANY solutions.  Then then the lines will never cross and there is NO SOLUTION.

Aim #2.3: How do we solve systems of equations by elimination?  Practice: a) 6x + 2y = 9 5x -2y = 2 c) 5x – 2y = -2 4y + 3x = -22 b)6y – 2x = 6 3y- 3x = 10

Summary: Answer in complete sentences :  Explain the solution you may get if you have an infinitely many solution system.