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Solve Systems of Linear Equations Using Elimination Honors Math – Grade 8

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Elimination using Addition Sometimes adding two equations together will eliminate one variable. Using this step to solve a system of equations is called elimination. +

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1 Since the coefficients of the y terms, -5 and 5, are additive inverses (opposites), you can eliminate these terms by adding the equations. The solution is (3, 5) + The y variable is eliminated because -5 + 5 = 0 Solve the equation 2. Now substitute x = 3 in either equation and solve. 1. Write the equations in column form and add.

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2 Since the coefficients of the x terms, 4 and -4, are additive inverses (opposites), you can eliminate these terms by adding the equations. The solution is (0, -1) + The x variable is eliminated because -4 + 4 = 0 Solve the equation 2. Now substitute y = -1 in either equation and solve. 1. Write the equations in column form and add.

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3 Since the coefficients of the s terms, 2 and -2, are additive inverses (opposites), you can eliminate these terms by adding the equations. The solution is (25, 12) + The s variable is eliminated because -2 + 2 = 0 Solve the equation 2. Now substitute j = 25 in either equation and solve. 1. Write the equations in column form and add.

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Elimination using Subtraction Sometimes subtracting one equation from another will eliminate one variable. -

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4 Since the coefficients of the t terms, 2 and 2, are the same, you can eliminate these terms by subtracting the equations. The solution is (4, -7) - The t variable is eliminated because 2 – 2 = 0 Solve the equation 2. Now substitute s = 4 in either equation and solve. 1. Write the equations in column form and subtract.

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5 Since the coefficients of the m terms, -1 and -1, are the same, you can eliminate these terms by subtracting the equations. The solution is (2, -1) - The m variable is eliminated because -1 - - 1 = 0 Solve the equation 2. Now substitute n = -1 in either equation and solve 1. Write the equations in column form and subtract.

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6 Since the coefficients of the w terms, 2.5 and 2.5, are the same, you can eliminate these terms by subtracting the equations. The solution is (2, -1) - The w variable is eliminated because 2.5–2.5 = 0 Solve the equation 2. Now substitute n = -1 in either equation and solve 1. Write the equations in column form and subtract.

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7 Let x represent the first number and y represent the second number. Translate each sentence into an algebraic equation. The numbers are 5 and 8. + The y variable is eliminated because 1 + - 1 = 0 Solve the equation x = 5 2. Now substitute x = 5 in either equation and solve. 2x + y=18 2(5) + y=18 10 + y=18 y=8 1. Write the equations in column form and add. Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers.

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