How do I equate coefficients?I got the problem into this form: A + B = 0 C − B = 1 8 A + 4 B − C + D = 10 − 4 B + 4 C − D + E = 3 16 A − 4 C − E = 36I really don't know what to do after that. I suck at equating coefficients. It never makes sense to me. Please help and provide steps and a good explanation. Thank you.

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How do I equate coefficients?I got the problem into this form:  A  +  B  =  0  C  −  B  =  1  8  A  +  4  B  −  C  +  D  =  10  −  4  B  +  4  C  −  D  +  E  =  3  16  A  −  4  C  −  E  =  36I really don&#039;t know what to do after that. I suck at equating coefficients. It never makes sense to me. Please help and provide steps and a good explanation. Thank you.

Paskcreessy4k5 · Accepted Answer

(1)                    A        +        B        =        0                                (2)                    C        −        B        =        1                                (3)                    8        A        +        4        B        −        C        +        D        =        10                                (4)                    −        4        B        +        4        C        −        D        +        E        =        3                                (5)                    16        A        −        4        C        −        E        =        36            It is best to solve these types of problems by getting all of the variables in terms of one variable. In this case we choose   B because it looks like it will be easier.From   (  1  ), we get that   A  =  −  BFrom   (  2  )  , we get that   C  =  1  +  BPlugging this into   (  3  )  :  8  (  −  B  )  +  4  B  −  (  1  +  B  )  +  D  =  10    ⟹    −  5  B  +  D  =  11    ⟹    D  =  11  +  5  BPlugging this into   (  4  )  :  −  4  B  +  4  (  1  +  B  )  −  (  11  +  5  B  )  +  E  =  3    ⟹    −  5  B  +  E  =  10    ⟹    E  =  10  +  5  BPlugging this into   (  5  )  :  16  (  −  B  )  −  4  (  1  +  B  )  −  (  10  +  5  B  )  =  36    ⟹    −  25  B  =  50    ⟹    B  =  −  2Then we can calculate all the other variables which are in terms of   B:  A  =  2  ,    C  =  −  1  ,    D  =  11  −  10  =  1  ,    E  =  10  −  10  =  0You can plug the variables back in to any of the equations to check that the answer is correct.

vidamuhae · Accepted Answer

Adding equation (1) and (2),  A  +  C  =  1  C  =  1  −  AAlso from equation (1),  B  =  −  AFrom equation (3),  8  A  +  4  (  −  A  )  −  (  1  −  A  )  +  D  =  10  8  A  −  4  A  −  1  +  A  +  D  =  10  5  A  +  D  =  10  +  1  5  A  +  D  =  11  D  =  11  −  5  AFrom equation (4),  4  (  −  B  +  C  )  −  D  +  E  =  3  4  (  1  )  −  D  +  E  =  3  E  −  D  =  −  1  E  =  D  −  1  E  =  11  −  5  A  −  1  E  =  10  −  5  ANow each variable has value in terms of A. Hope now you can proceed.

How do I equate coefficients? I got the problem into this form: A+B=0 C−B=1 8A+4B−C+D=10 −4B+4C−D+E=3 16A−4C−E=36 I really don't know what to do after that. I suck at equating coefficients. It never makes sense to me. Please help and provide steps and a good explanation. Thank you.

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