September 11, 2014 Page 18 – 19 in Notes

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Presentation transcript:

September 11, 2014 Page 18 – 19 in Notes Elimination Method September 11, 2014 Page 18 – 19 in Notes

Warm-Up (page 18) How many values do you solve for when solving a system of linear equations? How is the solution to a system of linear equations written? Is (3, 4) a solution to the following system? Explain why or why not. How about (3, -4)? 7x + 3y = 9 4x + 4y = -4

Solving Systems using Elimination Title of Notes – pg. 19

Essential Question How do I use the elimination method to solve systems of equations?

The immediate goal of the “elimination” method is to cancel out one of the variables by adding the two equations together. To do this, you need opposite coefficients in the two equations for the variable you are trying to eliminate. ALWAYS start elimination from standard form (Ax + By = C)!

Elimination Steps Multiply each equation by the coefficient in the other equation for the variable you are trying to eliminate. (Use a negative where necessary so that you end up with opposites.) Add the two equations and solve for the remaining variable. (Make sure you have opposites that add to zero.)

Elimination Steps (cont.) Now, substitute your value into an original equation and solve for the rest of your coordinate pair. Check your point in both original equations.

Solve the system of equations using the elimination method. Ex. 1 12x + 8y = -8 solution: _______ 3x + 4y = 2 Multiply the equations by the correct coefficients so the x’s will cancel. 3(12x + 8y) = -8(3) (Step 1) -12(3x+4y) = 2(-12) Now our system of equations is: 36x + 24y = -24 -36x – 48y = -24 Add the equations together: (Step 2) y = 2 -24y = -48

12x + 8y = -8 solution: _______ 3x + 4y = 2 (2, -2) Plug y = 2 into an original equation: (Step 3) 12x + 8(2) = -8 12x + 16 = -8 12x = -24 x = -2 So, the solution is (-2, 2). Now check: (Step 4) OR 3x + 4(2) = 2 3x + 8 = 2 3x = -6 x = -2 12(-2) + 8(2) = -8 -24 + 16 = -8 -8 = -8 3(-2) + 4(2) = 2 -6 + 8 = 2 2 = 2

Solve the system of equations using the elimination method. 4x – 3y = 14 Solution: _________ 2x + 5y = -6

Solve the system of equations using the elimination method. 11x – 3y = 104 Solution: _________ 2x – 5y = -60

Reflection Which method of solving systems (substitution or elimination) is easier for you and why?