Section 8.2 Solving Linear Systems by Elimination

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Presentation transcript:

Section 8.2 Solving Linear Systems by Elimination Pre-calculus 11 Chapter 8.2

I) Solving Linear Systems By Elimination Goal: Add or subtract the equations so that you will cancel out one variable Find the LCM for the coefficients for ‘x’ Multiply each equation so that the coefficients of ‘x’ become the LCM Add/subtract the equations to cancel out one variable Solve Plug the answer back into the original equation and solve for the 2nd variable

EX: SOLVE THE SYSTEM BY ADDITION/SUBTRACTION 1. Coefficients of “x” 2. LCM: 12 3. Subtract the equations 4. Solve for the remaining variable 5. Plug into original equation to solve for 2nd variable

PRACTICE: SOLVE BY ADDITION/SUBTRACTION 1. Coefficients of “y” 2. LCM: 12 3. Subtract the equations 4. Solve for the remaining variable 5. Plug into original equation to solve for 2nd variable

PRACTICE: SOLVE BY ADDITION/SUBTRACTION Multiply all terms by LCD to cancel out your denominators Coefficients of “x” Add the equations

Properties of Linear Systems: Multiplying an entire equation by a constant does not change the solution Adding or subtracting two equations does not change the solution Slope and Y-intercept are still the same

Solving Systems Involving Quadratics Eliminate one of the variables by adding/subtracting the two equations After the two equations are combined, factor or use the quadratic formula to solve the equation Use this answer to solve the other variable The solution to this system is

Practice: Solve this system by elimination Solve for “y” The solution to this system is

Homework: P317 #5(aced), 7, 8, 14 – 17a (18**)