Question 82581
{{{x + 2y >= 3}}}
{{{2x - 3y >= 6}}}
{{{ graph( 300, 300, -10, 10, -10, 10, (3-x)/2,(2x-6)/3 ) }}}
The solution is the V-shaped region to the right of where both
lines touch the x-axis at (3,0)
This is found by solving each inequality for y
{{{x + 2y >= 3}}}
{{{2y >= 3 - x}}}
{{{y >= (3 - x)/2}}} 1st solution
{{{2x - 3y >= 6}}}
{{{-3y >= 6 - 2x}}}
{{{y <= (2x - 6)/3}}} 2nd solution
Note that the inequality sign changed direction when I divided
both sides by -3
check solution
Does (3,0) satisfy both equations?
yes
Pick any point in the V-shaped region, like (6, 1)
{{{x + 2y >= 3}}}
{{{2x - 3y >= 6}}}
and
{{{6 + 3 >= 3}}}
{{{6 - 3 >= 3}}}
both are true. try some others