Intermediate Algebra for College Students (7th Edition)

For the first equation $2x+3y=6$, the $x$ and $y$ intercepts are found as $(3,0)$ and $(0,2)$ by substituting $0$ for $y$ and $x$ values in the equation respectively. Similarly, for the second equation $4x=-6y+12$, the $x$ and $y$ intercepts are found as $(3,0)$ and $(0,2)$ by substituting $0$ for $y$ and $x$ values in the equation respectively. Now, graph each equation as a line passing through the intercepts. It is observed that the both lines coincides with each other. It indicates that the system has infinitely many solutions. The graph is as below.