Question 143883
First, get your equations into the slope-intercept form: y = mx+b, to facilitate the graphing.
1) {{{3x-9y = 54}}} Subtract 3x from both sides.
{{{-9y = -3x+54}}} Now divide both sides by -9.
{{{y = (1/3)x-6}}}
2) {{{2x-6y = -2}}} Subtract 2x from both sides.
{{{-6y = -2x-2}}} Now divide both sides by -6.
{{{y = (1/3)x+1/3}}}
Now graph the two equations.
{{{graph(400,400,-5,20,-7,5,(1/3)x-6,(1/3)x+1/3)}}}
As you can see, the lines are parallel, thus they have no point in common. The system has no solution and is therefore an inconsistent system.