Answer
the ordered pair \[\left( 2,5 \right)\] is not the solution of the system of equations.
Work Step by Step
Multiply equation second with \[-2\]and add it with first equation, thus
\[\begin{align}
& \left( x+4y=16 \right)\times -2 \\
& -2x-8y=-32 \\
\end{align}\]
Now, add first and above equation to eliminate\[x\]as:
\[\begin{align}
& \left( 2x+3y \right)+\left( -2x-8y \right)=17+\left( -32 \right) \\
& 3y-8y=-15 \\
& -5y=-15 \\
& y=3
\end{align}\]
Now, substitute the value of\[y=3\]in the first equation to get the value of \[x\]as:
\[\begin{align}
& 2x+3\left( 3 \right)=17 \\
& 2x+9=17 \\
& 2x=8 \\
& x=4
\end{align}\]
Thus, the ordered pair \[\left( 4,3 \right)\]is the solution of the system of equations.
Hence, the ordered pair \[\left( 2,5 \right)\] is not the solution of the system of equations.
