Solution:
\( \displaylines{\text{Setting each equation to zero yields two straight lines, we find the intersection.}\\ y_1=\frac17\left(4x+2\right),y_2=\frac16\left(1-3x\right)\\ y_1=y_2\implies x=-\frac19\implies y=\frac29\\ \left(-\frac19,\frac29\right)} \)