Given:
y<2x+4" ".......................Eqn(1)
-3x-2y>=6" ".....................Eqn(2)
color(blue)("Converting "Eqn(2)" into standardised form ")
Consider Eqn(2)
Add 2y to both sides and subtract 6 from both sides giving:
-3x-6>=2y
Divide both sides by 2
-3/2 x-6/2>=y
Write the order as per convention
y<=-3/2x-3" "..........Eqn(2_a)
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Plot them color(magenta)(ul("as if they were"))
y=-3/2 x-3 color(white)("dddd") ->color(white)("dddd")"really is: " y<2x+4 " "Eqn(2_a)
Feasible solution area is below color(white)()"and "ul(color(red)("including the solid line"))color(white)("d") Eqn(2_a)
and:
y=2x+4 color(white)("dddd") ->color(white)("dddd")"really is: " y<2x+4" "Eqn(1)
Feasible solution area is below and
color(red)(ul("excluding the dotted line "))Eqn(1)
The solution area is where these two are coincidental (coincide).
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color(blue)("Determine key point - Intersection of the two lines")
y=2x+4 " "............Eqn(1)
y=-3/2 x-3" "......Eqn(2_a)
Eqn(1)-Eqn(2) to 'get rid' of the y's
0=7/2x+7
color(green)(x=-7xx2/7=-2)
Substitute x=-2 in Eqn(2_a) giving:
y=(-3/2)(-2)-3 = +3-3=0
color(blue)(ul(bar(| color(white)(2/2) "Intersection"->(x,y)=(-2,0)color(white)(2/2) |))
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color(blue)("Determine key point - axis intercepts for "y<2x+4)
Set y=2x+4
Set x=0 ->
color(blue)(bar(ul(|color(white)(2/2)y_("intercept")=4color(white)(2/2)|))
Set y=0 -> color(blue)(ul(bar(|color(white)(2/2) x_("intercept")=-2color(white)(2/2)|))
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color(blue)("Determine key point - axis intercepts for "-3x-2y>=6)
Eqn(2_a)->y<=-3/2x-3
Set y=-3/2x-3
Set x=0 ->color(blue)( ul(bar(| color(white)(2/2)y_("intercept")= -3color(white)(2/2)|)))
Set y=0->color(blue)( ul(bar(| color(white)(2/2)x_("intercept")= -2color(white)(2/2)|)))
![Tony B]()
Tony B
