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Transcript
8.4 Solve Linear Systems by Elimination Using Multiplication Some systems are not easily solved by adding or subtracting the equations. You have to multiply to create opposite coefficients (LCM) first. For example: The opposite coefficients are +4 and -4. In some cases, you may have to multiply BOTH equations first to create opposite coefficients. For example: 2x – 9y = 1 x 4 7x – 12y = 23 x – 3 8x – 36y = 4 -21x + 36y = -69 The opposite coefficients are - 36 and +36. Steps Step 1: Multiply one or both of the equations by a constant to create opposite coefficients. Step 2: Add the equations to eliminate (cancel) one variable. Step 3: Solve this equation for the remaining variable. Step 4: Substitute in one of the original equations to find the value of the other variable. Step 5: Write the solution as an ordered pair. Solve each system. Ex 1: 3x - 3y = 21 8x + 6y = -14 Ex 2: 5y = 9x - 8 -20x + 10y = -10 Ex 3: 2 x + 3y = -34 3 x − 1 y = -1 2 Ex 4: 7x + 2y = 26 10x – 5y = -10 Methods for Solving Linear Systems When you want to see the intersection Graphing When one equation is easily solved for x or y Substitution y = 4 – 2x 4x + 2y = 8 Elimination Using Addition 4x + 7y = 15 6x – 7y = 5 When the coefficients of one variable are opposites Elimination Using Subtraction (Multiply by -1) 3x + 5y = -13 3x + 2y = -5 When the coefficients of one variable are the same Elimination 9x + 2y = 38 3x – 5y = 7 When no corresponding coefficients are the same or opposites State the best method to use to solve the following linear systems. Ex 5: -2x + 5y = 14 8x + 5y = 94 Ex 6: 4x = -21 + y -3x + 7y = 51 Ex 7: -3x + 11y = -38 2x = -40 -9y Ex 8: 4.5x + 0.5y = 48.5 2.5x = 0.5y + 14.5