Question

Reduce the system of linear equations to upper triangular form and solve. \(\begin{cases}5x-3y=2\\2x+7y=3\end{cases}\)

Answer 1

System becomes
\(5x-3y=2\)
\(\frac{6}{5}y+7y=-\frac{4}{5}+3\)
\(\frac{41}{5}y=\frac{11}{5}\)
\(y=\frac{11}{5}\cdot\frac{5}{41}=\frac{11}{41}\)
\(5x-3\cdot\frac{11}{41}=2\)
\(5x-\frac{33}{41}=2\)
\(5x=2+\frac{33}{41}=\frac{115}{41}\)
\(x=\frac{23}{41}\)
Result: \((x,y)=(\frac{23}{41},\frac{11}{41})\)