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Mr. Sims Addition Method - need to be able to add the 2 equations together and cancel out one of the variables 1. -3x + 2y = -6 5x – 2y = 18 2x Algebra 2 Section 10.2 C Addition Method add the 2 equations together and the y’s will cancel = 12 x=6 substitute into any equation with x and y to solve for y -3x + 2y = -6 -3(6) + 2y = -6 -18 + 2y = -6 +18 +18 2y = 12 y=6 Mr. Sims 2 . -1 3x + 5y = -16 3x – 2y = -9 multiply either top or bottom by a term, so that, when added a variable cancels out -3x – 5y = 16 3x – 2y = -9 -7y = 7 y = -1 substitute into any equation with x and y to solve for x 3x + 5y = -16 3x + 5(-1) = -16 3x – 5 = -16 +5 +5 3x = -11 11 x 3 Mr. Sims 3. 5 4x – 3y = 0 2 -10x + 7y = -2 multiply either top, bottom, or both by a term, so that, when added a variable cancels out 20x – 15y = 0 -20x + 14y = - 4 -y=-4 y=4 substitute into any equation with x and y to solve for x 4x – 3y = 0 4x – 3(4) = 0 4x – 12 = 0 +12 +12 4x = 12 x=3 Mr. Sims 4. 2 -6x + 5y = 4 7x – 10y = -8 -12x + 10y = 8 7x – 10y = -8 -5x = 0 x=0 substitute -6x + 5y = 4 -6(0) + 5y = 4 5y = 4 4 y 5 Mr. Sims 5. 4 -9x + 6y = 0 -3 -12x + 8y = 0 -36x + 24y = 0 36x – 24y = 0 0=0 always true infinitely many solutions Mr. Sims 6. 5 21x – 8y = -1 8 9x + 5y = 8 105x – 40y = -5 72x + 40y = 64 177x = 59 59 x 177 1 x 3 substitute 9x 5y 8 1 9 5y 8 3 3 + 5y = 8 -3 -3 5y = 5 y=1 Mr. Sims Solve using the addition method. 1.) 3x – 2y = 10 5x + 3y = -15 2.) 2y + 3x – 8.1 = 0 2x – 3y + 3.7 = 0 Algebra 2 Section 10.2 C Addition Method 3.) 5x – 7y + 16 = 0 x + 4y – 13 = 0 4.) 3x – 5y + 10 = 0 -9x + 15y = -30 Mr. Sims Any rebroadcast, reproduction, or other use of the pictures and materials from this site and presentations, without the express written consent of Mr. Sims, is prohibited. © Mr. Sims. All rights reserved. Mr. Sims