# Reduce the system of linear equations to upper triangular form and 2x+3y=5 Solve -y=-2+frac{2}{3}x

Reduce the system of linear equations to upper triangular form and
$2x+3y=5$
Solve
$-y=-2+\frac{2}{3}x$
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We are going to use following elementary row operations:
$\circ \text{Interchange i-th and j-th row:}{R}_{i}↔{R}_{j}$

$\left[\begin{array}{ccc}2& 3& 5\\ -\frac{2}{3}& -1& -2\end{array}\right]{R}_{2}\to 3\cdot {R}_{2}\left[\begin{array}{ccc}2& 3& 5\\ -2& -3& -6\end{array}\right]$
${R}_{2}\to {R}_{2}+{R}_{1}\left[\begin{array}{ccc}2& 3& 5\\ 0& 0& -1\end{array}\right]$
The second equation is 0=-1 . Contradiction , so the system doesnt have a solution.