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Name:__________________________________ Block:___ Date:______________ NOTES Notes: Solving Systems of Equations by Elimination When solving a linear system, you can sometimes add or subtract the equations to obtain a new equation in one variable. This method is called ELIMINATION. Step 1: Locate the variable with opposite or same coefficients Step 2: opposite coefficients →Add same coefficients → Subtract (multiply each term by -1 then add) Solve the resulting equation Step 3: Substitute in either original equation to find the value of the other variable. Step 4: Name the solution Step 5: Check your solutions in both equations Solve by linear combination (the elimination method) 1. 3x y 8 7x y 12 Example 1: 3x 4y 6 3x 2y 6 Example 2: 2x y 7 2x 7 y 31 4. 3x 5y 7 4x 5y 14 5. 5y 7x 3 7x y 9 7. 7x 2y 24 8x 2y 24 8. 5x 6y 10 5x 6y 46 9. 10. 9x 5y 23 12x 5y 19 11. 5x 6y 50 x 6y 26 12. 6. 1 y 8 2 3x y 5 4x 4 3 x y 1 5 5 2x 3y 7 x 2y 7 x 2y 7 Sometimes the coefficients do not match up as well! You need to multiply first in order to be able to eliminate one of the variables. 1. x y 2 2x 7 y 9 2. 6x 2 y 1 2 x 3 y 5 4. 2x 5 y 3 4 x 10 y 6 7. x y 0 1 1 x y 2 2 2 9. 18 x 6 y 24 3x y 2 5. 9 y 5x 5 3x 7 y 5 6. 8. 10. 3 3 x y 3 5 4 2 1 x y 8 5 3 9 x 15 y 24 6 x 10 y 16 4 x 8 y 10 x 2 y 6