Given data:
The first equation given is 5x+6y=14
The second equation given is 3x+5y=7.
Multiply first equation by 3 and second by 5 and then subtract second equation by first.
[tex]\begin{gathered} 3(5x+6y)-5(3x+5y)=3(14)-5(7) \\ 15x+18y-15x-25y=42-35 \\ -7y=7 \\ y=-1 \end{gathered}[/tex]Substitute -1 for y in the first equation.
[tex]\begin{gathered} 5x+6(-1)=14 \\ 5x=20 \\ x=4 \end{gathered}[/tex]