If $2x+3y=6$ and $4x-5y=1$, then find the value of $( x^y)$.

Given: Equations: $2x+3y=6$ and $4x-5y=1$

To do: To find the value of $( x^y)$.

$2x+3y=6$ .......$( 1)$

$4x-5y=1$ .......$( 2)$

On solving the above equations using elimination method, we will eliminate $x$ from both the equations.

Multiply $2$ to equation $( 1)$

$\Rightarrow 4x+6y=12$ .........$( 3)$

Subtract equation $( 2)$ from equation $( 3)$

$\Rightarrow 11y=11$

$\Rightarrow y=\frac{11}{11}$

$\Rightarrow y=1$

Now, substituting the value of $y$ in equation $( 1)$, we get

$x=\frac{3}{2}$

$\therefore ( x^y)=( \frac{3}{2})^1=\frac{3}{2}$