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Question
If x=6a+8b+9c;y=2b-3a-6c and z=c-b+3a ; find
(i) x+y+z (ii) x-y+z
(iii) 2x-y-3z (iv) 3y-2z-5x
If x=6a+8b+9c;y=2b-3a-6c and z=c-b+3a ; find
(i) x+y+z (ii) x-y+z
(iii) 2x-y-3z (iv) 3y-2z-5x
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Solution
(i)x=−6a+8b+9cy=−3a+2b−6c z=+3a−b+c––––––––––––––––––––Adding x+y+z=6a+9b+4c––––––––––––––––––––––––––– Ans.
(ii) x−y+z=(6a+8b+9c)−(2b−3a−6c)+(c−b+3a)=6a+8b+9c−2b+3a+6c+c−b+3a=6a+3a+3a+8b−2b−b+9c+6c+c=12a+5b+16c Ans.(iii)2x−y−3z=2(6a+8b+9c)−(2b−3a−6c)−3(c−b+3a)=12a+16b+18c−2b+3a+6c−3c+3b−9a=12a+3a−9a+16b+3b−2b+18c+6c−3c=6a+17b+21c Ans.(iv)3y−2z−5x=3(6a+8b+9c)−2(2b−3a−6c)−5(6a+8b+9c)=6b−9a−18c−2c+2b−6a−30a−40b−45c=−9a−6a−30a+6b+2b−40b−18c−2c−45c=−45a−32b−65c Ans.
(i)x=−6a+8b+9cy=−3a+2b−6c z=+3a−b+c––––––––––––––––––––Adding x+y+z=6a+9b+4c––––––––––––––––––––––––––– Ans.
(ii) x−y+z=(6a+8b+9c)−(2b−3a−6c)+(c−b+3a)=6a+8b+9c−2b+3a+6c+c−b+3a=6a+3a+3a+8b−2b−b+9c+6c+c=12a+5b+16c Ans.(iii)2x−y−3z=2(6a+8b+9c)−(2b−3a−6c)−3(c−b+3a)=12a+16b+18c−2b+3a+6c−3c+3b−9a=12a+3a−9a+16b+3b−2b+18c+6c−3c=6a+17b+21c Ans.(iv)3y−2z−5x=3(6a+8b+9c)−2(2b−3a−6c)−5(6a+8b+9c)=6b−9a−18c−2c+2b−6a−30a−40b−45c=−9a−6a−30a+6b+2b−40b−18c−2c−45c=−45a−32b−65c Ans.
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