# Reduce the system of linear equations to upper triangular form and solve. 5x+2y=8, -x+3y=9

Reduce the system of linear equations to upper triangular form and solve.
5x+2y=8
-x+3y=9

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Fatema Sutton
System becomes: 5x+2y=8
$$\displaystyle{\left(\frac{{2}}{{5}}\right)}{y}+{3}{y}={\left(\frac{{8}}{{5}}\right)}+{9}$$
$$\displaystyle{\left(\frac{{17}}{{5}}\right)}{y}=\frac{{53}}{{5}}$$
Add 1/5 times first equation to second.
$$\displaystyle{y}={\left(\frac{{53}}{{5}}\right)}{\left(\frac{{5}}{{17}}\right)}=\frac{{53}}{{17}}$$
$$\displaystyle{5}{x}+{2}{\left(\frac{{53}}{{17}}\right)}={8}$$
$$\displaystyle{5}{x}={8}-{\left(\frac{{106}}{{17}}\right)}$$
$$\displaystyle{5}{x}=\frac{{30}}{{17}}$$
$$\displaystyle{x}=\frac{{6}}{{17}}$$
Solve the system.
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content_user

Answer is given below (on video)