Answer
$x=3$
Work Step by Step
Because we are told that $y_{1}=y_{2}$, we may set the two equations equal to one another and solve:
$7(3x-2)+5=6(2x-1)+24$
$21x-14+5=12x-6+24$
$21x-9=12x+18$
$21x-12x=18+9$
$9x=27$
$x=3$
The two equations describe a pair of intersecting lines, so there is only one solution.