Question 300413
The quickest way to graph a line is to find the intercepts. 
To find the x-intercept, set y=0 and solve for x.
{{{3x+y=5}}}
{{{3x+0=5}}}
{{{3x=5}}}
{{{x=5/3}}}
(5/3,0)
To find the y-intercept, set x=0 and solve for y.
{{{3x+y=5}}}
{{{0+y=5}}}
{{{y=5}}}
(0,5)
Plot those points and graph the first line.
{{{drawing(300,300,-3,6,-3,6,grid(1),circle(5/3,0,.25),circle(0,5,.25),graph(300,300,-3,6,-3,6,-3x+5))}}}
.
.
.
Do the same for the next line.
To find the x-intercept, set y=0 and solve for x.
{{{-2x+3y=4}}}
{{{-2x+0=4}}}
{{{x=-2}}}
(-2,0)
To find the y-intercept, set x=0 and solve for y.
{{{-2x+3y=4}}}
{{{0+3y=4}}}
{{{y=4/3}}}
(0,4/3)
{{{drawing(300,300,-3,6,-3,6,grid(1),
circle(-2,0,.25),
circle(0,4/3,.25),
circle(5/3,0,.25),circle(0,5,.25),graph(300,300,-3,6,-3,6,(2x+4)/3,-3x+5))}}}
.
.
.
From looking at the graph, it's apparent that the intersection point is (1,2). 
Verify by plugging into the original equations.
{{{3x+y=5}}}
{{{3(1)+2=5}}}
{{{3+2=5}}}
{{{5=5}}}
True
{{{-2x+3y=4}}}
{{{-2(1)+3(2)=4}}}
{{{-2+6=4}}}
{{{4=4}}}
True
Solves both equations, its a good solution.
(1,2)