Question

Select the correct answer.What is the solution to this system of equations?-a – 3b + 4c = 35a – 8b + 5c = 275a – 25 + 6c = 1

Answer 1

Given,

The linear equations are,

`\begin{gathered} -a-3b+4c=3 \\ 5a-8b+5c=27 \\ 5a-25+6c=1 \end{gathered}`

Taking equation first as,

`\begin{gathered} -a-3b+4c=3 \\ -a=3-4c+3b \\ a=4c-3b-3\ldots\ldots\ldots\ldots\ldots\text{.(i)} \end{gathered}`

Substituting the value of a from equation (i) to equation second,

`\begin{gathered} 5a-8b+5c=27 \\ 5(4c-3b-3)-8b+5c=27 \\ 20c-15b-15-8b+5c=27 \\ 25c-23b=42 \\ -23b=42-25c \\ b=(25c-42)/(23)\ldots\ldots\ldots\ldots\ldots\text{.}(ii) \end{gathered}`

Subsituting the value of b in equation (i),

`\begin{gathered} a=4c-3b-3 \\ a=4c-3((25c-42)/(23))-3 \\ a=(92c-75c+126-69)/(23) \\ a=(17c+57)/(23)\ldots\ldots\ldots.\ldots\ldots\ldots\ldots\ldots\text{.(i}ii) \end{gathered}`

Subsituting the value of a from equation (iii) to last equation,

`\begin{gathered} 5a-25+6c=1 \\ 5((17c+57)/(23))+6c=1+25 \\ 85c+285+138c=598 \\ 223c=313 \\ c\approx1.40 \end{gathered}`

Suubstituting the value of c in equation (ii),

`\begin{gathered} b=(25(3.42)-12)/(23) \\ b\approx3.20 \end{gathered}`

Subsituting the value of c in equation (iii),

`\begin{gathered} a=(17(3.42)-33)/(23) \\ a\approx1.09 \end{gathered}`