# SOLUTION: Solve each system by the addition method. 3/7x+5/9y=27 1/9x+2/7y=7 and 3x-2.5y=7.125 2.5x-3y=7.3125

Algebra ->  -> SOLUTION: Solve each system by the addition method. 3/7x+5/9y=27 1/9x+2/7y=7 and 3x-2.5y=7.125 2.5x-3y=7.3125      Log On

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 Question 175921: Solve each system by the addition method. 3/7x+5/9y=27 1/9x+2/7y=7 and 3x-2.5y=7.125 2.5x-3y=7.3125Answer by Alan3354(34679)   (Show Source): You can put this solution on YOUR website!Solve each system by the addition method. 3/7x+5/9y=27 1/9x+2/7y=7 Since it says "linear systems" I'll assume 3/7x means (3/7)x (3x/7) + (5y/9) = 27 Do them like this to avoid ambiguities. (x/9) + (2y/7) = 7 Multiply both eqns by 63 to eliminate fractions. 27x + 35y = 1701 7x + 18y = 441 Multiply the 1st eqn by 7 and the 2nd by 27 to get 189x in both 189x + 245y = 11907 189x + 486y = 11907 Subtract eqn 2 from eqn 1 0x - 241y = 0 y = 0 x = 11907/189 x = 63 ------------- and 3x-2.5y=7.125 2.5x-3y=7.3125 -------------- Multiply both by 16 48x - 40y = 114 40x - 48y = 117 All integers now Multiply the 1st eqn by 5, the 2nd by 6 240x - 200y = 570 240x - 288y = 702 Subtract the 2nd from the 1st 0x + 88y = -132 y = -1.5 ------------- Sub for y into 2.5x-3y=7.3125 2.5x -3*(-1.5) = 7.3125 2.5x + 4.5 = 7.3125 2.5x = 2.8125 x = 1.125