document.write( "Question 82581: Solve the following system of linear inequalities by graphing:\r
\n" ); document.write( "\n" ); document.write( "x+2y>(with a line under it)3
\n" ); document.write( "2x-3y>(with a line under it)6 \n" ); document.write( "

Algebra.Com's Answer #59182 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x+%2B+2y+%3E=+3\"$
\n" ); document.write( " $\"2x+-+3y+%3E=+6\"$
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%283-x%29%2F2%2C%282x-6%29%2F3+%29+\"$
\n" ); document.write( "The solution is the V-shaped region to the right of where both
\n" ); document.write( "lines touch the x-axis at (3,0)
\n" ); document.write( "This is found by solving each inequality for y
\n" ); document.write( " $\"x+%2B+2y+%3E=+3\"$
\n" ); document.write( " $\"2y+%3E=+3+-+x\"$
\n" ); document.write( " $\"y+%3E=+%283+-+x%29%2F2\"$ 1st solution
\n" ); document.write( " $\"2x+-+3y+%3E=+6\"$
\n" ); document.write( " $\"-3y+%3E=+6+-+2x\"$
\n" ); document.write( " $\"y+%3C=+%282x+-+6%29%2F3\"$ 2nd solution
\n" ); document.write( "Note that the inequality sign changed direction when I divided
\n" ); document.write( "both sides by -3
\n" ); document.write( "check solution
\n" ); document.write( "Does (3,0) satisfy both equations?
\n" ); document.write( "yes
\n" ); document.write( "Pick any point in the V-shaped region, like (6, 1)
\n" ); document.write( " $\"x+%2B+2y+%3E=+3\"$
\n" ); document.write( " $\"2x+-+3y+%3E=+6\"$
\n" ); document.write( "and
\n" ); document.write( " $\"6+%2B+3+%3E=+3\"$
\n" ); document.write( " $\"6+-+3+%3E=+3\"$
\n" ); document.write( "both are true. try some others \n" ); document.write( "

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