Ch7

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 * Chapter 7: Systems of Equations and Inequalities**

Ex. y=5x+2 y=6x+4 __As long as they are have the same variables and are 'grouped' it is a system of linear equations.__ They are generally grouped vertically like shown above.
 * A system of linear equations **consists of two or more linear equations in the same variables.


 * It doesn't //have// to be in slope intercept form, I just personally prefer it that way.**

5x+3y=7 7x+2y=9 <---This is still a system of linear equations.

Ex. y=2x+3, y=3x+2, (1,5), (1,5) __w__ __orks for both equations__ therefore it is considered a solution of this system of linear equations.
 * A Solution of a System of Linear Equations **in two variables is an ordered pair that satisfies each equation in the system.
 * It has to work for both equations.**

Methods for Solving Systems of Equations Graphing Substitution Elimination

// (Also known as Matrices) // Start up your calculator and hit menu After that, hit Equa Now you are at the cheat screen. Press F1, then F1 again to get 2 unknowns. As long as they are in standard form, this should be easy. Take the co-efficients and put them in the matrices. The X's for both equations go in the 'A' column, the Y's go in the 'B' column. The sum or difference of the equations goes in the 'C' column. Press solve. You will get a matrix with two numbers, one on top the other on bottom. The one on top is your X, the bottom is your Y, of which you would plug in like this: (x,y) That is the solution.
 * Solving Systems using the Casio Cheat Method **

**Example:** // 4x+y=8 (1) // // 2x-3y=18 (2) // // To graph these equations, you would generally convert them into slope intercept form, (but you can graph in standard form). // // Slope Intercept is y=mx+b. m=Slope b= y-intercept (where the line crosses the y axis). // What these equations look like in slope intercept form: y=-4x+8 (1) y=2/3x-6 (2) After you graph these two lines, find where they intersect and that is the solution to this system linear equations. The solution to this system of linear equations is (3,-4).

// The difference of 2 numbers is 4, the sum of their values is also 14, write the equation. // Here, we see that the difference, meaning subtraction, of 2 numbers, which we don't know, is 4. Since we don't know these numbers, we write them as variables. x-y=4 is how we would write the first part. The second part says the sum of the //same// numbers is also 14. Similarly, we would write the equation like this x+y=14. Therefore, our system is x-y=4, x+y=14. // A solution to this can be found by doing any of the above methods. // I found the solution to be (9,5).
 * Word Problem Example: **

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