Chapter 2 Review Linear equations and inequalities.

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Presentation transcript:

Chapter 2 Review Linear equations and inequalities

Solving Systems of Equations (2 Variables) By graphing : Rewrite equation in y=mx+b format Then graph both equations Find the point of intersection

By Elimination: cancel a variable by multiplying both equations by a constant Add the remaining terms You are left with your new equation Solve this equation for one variable Plug this answer into either of the original equations to find the other variable Write in (x,y) format

By Substitution: Use this method when you can easily solve for one variable (when one of the variables has a coefficient of 1) Solve the simple (coefficient of 1) equation for one variable (y= c x or x= c y) Plug this answer into the other equation Then, plus the answer you get into the simple equation, and find the other variable

Modifications: If you have 3 variables (x,y,z): You cannot do graphing on a normal graph (there is no z plane) Elimination: try and multiply the equations so that you can eliminate one variable altogether, then work with 2 equations at a time to solve for the other variables, eliminating another variable and eventually solve for one variable, then another, then the last one. Basically, you have to do elimination twice instead of just once. Substitution: Use this when one equation has 2 or fewer variables. Solve the simple equation, then plug that into another equation and you end up with 2 variables, then plug that into the next equation and solve for one variable. Then, go backwards and plug that information into remaining equations.

Inequalities: By graphing: Use the same process as with an = sign, but your answer will include the entire region that is greater to, great/equal to, less than/equal to, or less than the equation graphed according to the sign of the equation. If you have 3 linear equations, it’s the area bound by the lines. There is no solution if there is no ordered pair that satisfies both equations or if the shaded area of both equations do NOT overlap.

Bibliography Advanced Mathematical Concepts textbook by Glencoe/McGraw hill