We are given the following system of equations
[tex]\begin{gathered} 2x-3y=4\quad eq.1 \\ 2x+8y=11\quad eq.2 \end{gathered}[/tex]
We are asked to find out if the ordered pair (5, 2) is a solution to the given system of equations.
Let us substitute the given ordered pair into both equation and check if it satisfies both equations.
Substitute x = 5 and y = 2 into eq.1
[tex]\begin{gathered} 2x-3y=4\quad eq.1 \\ 2(5)-3(2)=4 \\ 10-6=4 \\ 4=4\quad (\text{satisfied)} \end{gathered}[/tex]
Now, substitute x = 5 and y = 2 into eq.2
[tex]\begin{gathered} 2x+8y=11\quad eq.2 \\ 2(5)+8(2)=11 \\ 10+16=11 \\ 26\ne11\quad (\text{not satisfied)} \end{gathered}[/tex]
As you can see, the given ordered pair do not satisify both of the equations therefore, it is not a valid solution to the given system of equations.
