# Reduce the system of linear equations to upper triangular form and solve. begin{cases}5x-3y=22x+7y=3end{cases}

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

2021-02-23
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: $$(x,y)=(\frac{23}{41},\frac{11}{41})$$

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