we have the equations
[tex]\begin{gathered} y_1=2(4x-7)-8 \\ y_2=5(x-3)+14 \end{gathered}[/tex]Equate y1 and y2
[tex]\begin{gathered} 2(4x-7)-8=5(x-3)+14 \\ solve\text{ for x} \\ 8x-14-8=5x-15+14 \\ 8x-22=5x-1 \\ 8x-5x=-1+22 \\ 3x=21 \\ x=7 \end{gathered}[/tex]