Find the sum of all elements in X where 2X−Y=3−30332,2Y+X=415−14−4

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answer is 5.

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Detailed Solution

Given,2X−Y=3-30332On multiplying both sides by 2, we get4X−2Y=23−30332;4X−2Y=6−60664----ialso given X+2Y=4 1 5−1 4 −4----iiAdding Eqs. (i) and (i), we get 5X=6−60664+415−14−4=6+4−6+10+56−16+44−4=10−555100X=1510−555100⇒X=2−11120Putting the value of X in Eq. (i), we get2−11120+2Y=415−14−4⇒ 2Y=415−14−4−2−11120=4−21+15−1−1−14−2−4−0=224−22−4Y=112−11−2∴ X=2−11120 and Y=112−11−2

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