Solve the inequalities graphically in two-dimensional plane
1. $x+y<5$
Consider $x+y=5$
(i) put x=0,
$(0)+y=5$
$y=5$
(ii) put y=0,
$x+(0)=5$
$x=5$
Draw the line with values (0,5) and (5,0). Since inequality is $<$, draw dotted line.
Consider origin (0,0)
$(0)+(0)=0< 5$, which true
step 4: Since (0,0) satisfies the given inequality, shade the portion which contain (0,0).
2.  $2x+y\geq 6$
Consider, $2x+y= 6$
(i) put x=0,
$2(0)+y=6$
$y=6$
(ii) put y=0,
$2x+(0)=6$
$x=3$
Draw the line with values (0,6) and (3,0). Since inequality is $\geq$, draw thick line.
Consider origin (0,0)
$2(0)+(0)=0\geq 6$, which is not true
step 4: Since (0,0) does not satisfy the given inequality, shade the portion which does not contain (0,0)
3. $3x+4y\leq 12$
Consider, $3x+4y=12$
(i) put x=0,
$3(0)+4y=12$
$y=3$
(ii) put y=0,
$3x+4(0)=12$
$x=4$
Draw the line with values (0,3) and (4,0). Since inequality is $\geq$, draw thick line.
Consider origin (0,0)
$3(0)+4(0)=0\leq 12$, which is true
step 4: Since (0,0) satisfies the given inequality, shade the portion which contain (0,0)
4.  $y+8\geq 2x$
Consider, $y+8= 2x$
 $y-2x=-8$
(i) put x=0,
$y-2(0)=-8$
$y=-8$
(ii) put y=0,
$0-2x=-8$
$x=4$
Draw the line with values (0,-8) and (4,0). Since inequality is $\geq$, draw thick line.
Consider origin (0,0)
$0-2(0)=0\geq -8$, which is true
step 4: Since (0,0) satifies the given inequality, shade the portion which contain (0,0)

5. $x-y\leq 2$
Consider, $x-y= 2$
(i) put x=0,
$(0)-y=2$
$y=-2$
(ii) put y=0,
$x-(0)=2$
$x=2$
Draw the line with values (0,-2) and (2,0). Since inequality is $\leq$, draw thick line.
Consider origin (0,0)
$(0)-(0)=0\leq 2$, which is true
step 4: Since (0,0) satisfies the given inequality, shade the portion which contain (0,0)
6. $2x-3y>6$
Consider, $2x-3y=6$
(i) put x=0,
$2(0)-3y=6$
$y=-2$
(ii) put y=0,
$2x-3(0)=6$
$x=3$
Draw the line with values (0,-2) and (3,0). Since inequality is $>$, draw dotted line.
Consider origin (0,0)
$2(0)-3(0)=0> 6$, which is not true
step 4: Since (0,0) does not satisfy the given inequality, shade the portion which does not contain (0,0)
7. $-3x+2y\geq -6$
Consider, $-3x+2y= -6$
(i) put x=0,
$-3(0)+2y=-6$
$y=-3$
(ii) put y=0,
$-3x+2(0)=-6$
$x=2$
Draw the line with values (0,-3) and (2,0). Since inequality is $\geq$, draw thick line.
Consider origin (0,0)
$-3(0)+2(0)=0\geq -6$, which is true
step 4: Since (0,0) satisfies the given inequality, shade the portion which
contain (0,0)
8. $3x-5y<30$
Consider, $3x-5y=30$
(i) put x=0,
$3(0)-5y=30$
$y=10$
(ii) put y=0,
$3x-5(0)=30$
$x=-6$
Draw the line with values (0,10) and (-6,0). Since inequality is $<$, draw dotted line.
Consider origin (0,0)
$3(0)-5(0)=0< 30$, which is true
step 4: Since (0,0) satisfies the given inequality, shade the portion which contain (0,0)
9.  $y<-2$
Consider, $y=-2$
Draw the line parallel to x-axis with value (0,-2). Since inequality is $<$, draw dotted line.
Consider origin (0,0)
$(0)=0<-2$, which is not true
step 4: Since (0,0) does not satisfy the given inequality, shade the portion which does not contain (0,0)
10. $x>-3$
Consider, $x=-3$
Draw the line parallel to y-axis with value (-3,0). Since inequality is $>$, draw dotted line.
Consider origin (0,0)
$(0)=0>-3$, which is true
step 4: Since (0,0) satisfies the given inequality, shade the portion which contain (0,0)
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