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Question

Solve for xandy

2x-1+y-24=2;32(x-1)+2(y-2)5=4720


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Solution

Step 1:Giving substitution

Given ,

2x-1+y-24=232(x-1)+2(y-2)5=4720

Let1x-1=Aandy-2=Bi.e;2A+B4=28A+B=8.............................(1)32A+25B=4720LCM=10,15A+4B10=472015A+4B=47230A+8B=47..............................(2)

Step 2 : Solving for A and B using elimination method

equation(1)×864A+8B=64..............................(3)equation(2)30A+8B=47.................................(2)

equation(3)-(2)34A=17A=1734=12SubstituteA=12in(1)18x12+B=84+B=8B=8-4=4

Step 3 : finding x and y

We have ,

A=1x-112=1x-1x-1=2x=3B=y-24=y-2y=4+2=6

Therefore the value of x=3andy=6


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