# Evaluate: {\text{begin}array l-6x+2y=-(9)/(2) } 9x-3y=(27)/(4)\text{end}array .

## Expression: $\left\{\begin{array} { l } -6x+2y=-\frac{ 9 }{ 2 } \\ 9x-3y=\frac{ 27 }{ 4 }\end{array} \right.$

Solve the equation for $x$

$\left\{\begin{array} { l } x=\frac{ 3 }{ 4 }+\frac{ 1 }{ 3 }y \\ 9x-3y=\frac{ 27 }{ 4 }\end{array} \right.$

Substitute the given value of $x$ into the equation $9x-3y=\frac{ 27 }{ 4 }$

$9\left( \frac{ 3 }{ 4 }+\frac{ 1 }{ 3 }y \right)-3y=\frac{ 27 }{ 4 }$

Solve the equation for $y$

$y \in ℝ$

The statement is true for any value of $y$ and $x$ that satisfy both equations from the system. Therefore, the solution in parametric form is

$\begin{array} { l }\left( x, y\right)=\left( \frac{ 3 }{ 4 }+\frac{ 1 }{ 3 }y, y\right),& y \in ℝ\end{array}$

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