Question

Solve the following simultaneous equations 5x+7y = 17 ; 7x+5y = 19
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Answer 1

`x=2.\ y=1`

Explanation:

`We\ are\ given\ the\ following\ pair\ of\ equations:\\5x+7y=17\\7x+5y=19\\Now,\\As\ the\ co-efficients\ of\ none\ of\ the\ algebraic\ terms\ match,\\We\ can\ take\ the\ LCM\ of\ their\ co-efficients;\\As\ the\ co-efficients\ of\ the\ x-terms\ are\ 5,7\ respectively;\\Their\ LCM\ is\ 35.`

`Hence,\\7(5x+7y)=7(17)\\-5(7x+5y)=-5(19)\\Hence,\\35x+49y=119\\-35x-25y=-95\\Hence,\\Adding\ the\ two\ equations\ we\ have:\\(35x+49y)+(-35x-25y)=(119)+(-95)\\(35x-35x)+(49y-25y)=119-95\\24y=24\\y=(24)/(24)=1`

`Now,\\Lets\ consider\ the\ First\ Equation:\\5x+7y=17\\Substituting\ y=1,\\5x+7*1=17\\5x+7=17\\5x=17-7\\5x=10\\x=(10)/(5)=2\\\\Together,\\x=2.\ y=1`