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Solving Linear Systems Using the Elimination Method

Learn how to solve the linear system of equations using the elimination method. This tutorial covers the equations -8x + 3y = 12 and 8x - 9y = 12. By adding the two equations together, we can eliminate one variable and solve for the remaining variable. The step-by-step solution leads to the values of x and y, ensuring clarity through each operation. Check your work for accuracy and understand how to apply these techniques to similar systems of equations.

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Solving Linear Systems Using the Elimination Method

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  1. Solve the linear system. Elimination Method: -8x + 3y=128x - 9y=12

  2. Solve the linear system. Solution: ( , ) Add the two equations together so that one variable is ELIMINATED. Do you have inverse or identical terms? + 3y=12 - 9y=12 -8x Inverse terms: Add + Yes! Inverse terms 8x Now, solve for the remaining variable. -6y = 24 -6 -6 -4 -4 y = Now what?

  3. Solve the linear system. Solution: ( , -4 ) -4 Substitute value into one of the original equations. -8x + 3y=128x - 9y=12 Elimination Method: ( ) -8 x + 3 • =12 y Solve. +12 -8 +12 -8 -8 x + -12 =12 -8 x =24 -3 -3 x =

  4. Solve the linear system. Solution: ( -3 , -4 ) -3 -4 Check!!!!! -8x + 3y=128x - 9y=12 Elimination Method: ( ( ) ) 8 - 9 x y • =12 -24 + 36 =12 12 =12

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