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REGION REPRESENTING INEQUALITIES IN TWO VARIABLES
Define The Inequalities Area
The regions representing inequalities in two variables:
Skills I!"rtant N"tes
To shade the region which satisfies the
inequalities of the form:
x > h, x < h,
x h and x h
x h is equivalent to
x > h and x = h
x h is equivalent to
x < h and x = hx > h : region on the ri#htand
x < h : region on the leftof the line x = h
Re#i"n
Skills I!"rtant N"tes
To shade the region which satisfies the
inequalities of the form :
y > k, y < ky and y k
y > k : region a$"%ethe line
y < k : region $el"&the line
Re#i"n
Skills I!"rtant N"tes
To shade the region which satisfies
inequalities of the form :
y > ax ! b
y < ax ! b
y ax ! b and
y ax ! b
y > ax ! b : region a$"%ethe line
y < ax ! b : region $el"&the line
The line y = ax ! b is shown as a dotted line for region
satisfying y > ax ! b or y < ax ! b
"bove, solid line
#elow, solid line
> "bove, dotted line
< #elow, dotted line
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E'a!les "f sha(in# the Re#i"n re!resentin# the inequalities #i%en
Skills I!"rtant N"tes
To shade the region which satisfies two or
three inequalities
$onsider the inequality one by one
%f & inequalities are given, draw the & corresponding
lines, then determine the region that satisfies both theinequalities
%f ' inequalities are given, you must draw ' straight
lines The region has ' boundaries
Re#i"n
x > ( x < )
y *& y x
x ! y )
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E'a Orientate( E'a!les
)* On the #ra!h in the ans&er s!a+e, sha(e the re#i"n &hi+h satisf- the three inequalities
', , 'y y x x y > +
Pada graf di ruang jawapan, lorekkan rantau yang memuaskan ketiga-tiga ketaksamaan
', , 'y y x x y > +
Ans&er
.
.
' / - 0.
- 0 '
+awapan ialah tindanan ketiga*
tiga enis lorekkan sebagaimanadi atas
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.* On the #ra!h in the ans&er s!a+e, sha(e the re#i"n &hi+h satisf- the three inequalities
', ', ' 'y y x y x> + +
Pada graf di ruang jawapan, lorekkan rantau yang memuaskan ketiga-tiga ketaksamaan
', ', ' 'y y x y x> + +
7a&a!an 2
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. x ! &y ) , y x , x
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3 &y x !) , x ! y . , y >*-
4 y&x ! ), y x and y < (
-/ &y x ! . , y *x , x
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--0n the graph provided, shaded the region which satisfies the three inequalities
y &x ! 3 , y x and y < 3
-&0n the graph in the answer space , shade the region which satisfies the three
inequalities y *&x ! -/ , x < ( and y -/
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Ans&er97a&a!an 2
0n the graph provided, shade the region which satisfies the three inequalities
- y &x 1 ., y *x ! . y
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. x ! &y ) , y x , x
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2 y *x ! . , y &x , y/
3 &y x !) , x ! y . , y >*-
4 y&x ! ), y x and y < (
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-/ &y x ! . , y *x , x
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