Question

Graph the system of inequalities
y>2x
2x + 3y≤6

Answer 1

convert your equations to slope-intercept form (the first one already is):\[\large\color{blue}{y>2x}\]\[2x+3y\le6\]\[3y\le-2x+6\]\[\large \color{blue}{y\le-{2\over3}x+2}\]use these to draw your graph. basic info:\[\color{blue}{y>2x}:\]\[y-intercept=0\]\[slope=2\]\[\color{blue}{y\le-{2\over3}x+2}:\]\[y-intercept=2\]\[slope=-{2\over3}\]**the line for \(y>2x\) should be dashed

now just plug in a point from one side of each lline and if it turns out true, that is where you should shade, if not, then shade on its other side:

i chose \((2,5)\)\[y>2x\]\[5>2(2)\]\[5>4~\sqrt{}\] \[y\le-{2\over3}x+2\]\[5\le-{2\over3}(2)+2\]\[5\le-{4\over3}+2\]\[5\le{2\over3}~X\]