x+y+1=0, 2x+x=2, 3y+x=9; infinitely many

x-y=2 ⇒ y=x-2
Table of solutions

We plot the points (2, 0) and 3,1) on the graph paper and join the same by a ruler to get the line which is the graph of the equation x-y=2

x=3y
x-3y+0=0
Comparing with ax+by+c=0, we get
a=1, b=-3, c=0.

2x-y+0=0; a=2, b=-1 and c=0

\(x-4=\sqrt{3}y\)=0; a=2, b=\(-\sqrt{3}\), c=-4

0x+5y-2=0

2x+0y-3=0

Since total number of voters who do not cast therir cotes=40%
Hence total number of voters who cast their votes =60%
Let the total numbers of voters are x and number of voters who cast their votes is y.
Then according to the question
y=60% of \(x=\frac{60}{100}x\)
Now, when c=100, then
y=60
when x=200, then y=120
when c=300, then y=180

By plotting the points (100,60), (200,120) (300,180) on the graph and by joining them, we get the graph of equation (1) as shown in fig. From the graph, we see that
(i) If 300 voters cast their votes, then total number of votes=500

(ii) If the total number of voters are 1000, then number of votes cast=600.
(iii) Everyone should cast his vote to elect an honest candidate.

If x=-2, y=6 is solution of equation
3ax+2by=6 then
3a(-2)+2b(6)=6
⇒ -6a+12b=6
⇒ -4+2b=1  ...(1)
Also,
2(a-1)+2(3b-4)=4
⇒ 2a-2+6b-8=4
⇒ 2a+6b=14
⇒ a+3b=7    ...(2)
Adding (1) and (2) we get
5b=8 ⇒ \(b={8\over 5}\)
Putting \(b={8\over 5}\) in (1), we get
-a+2\(\left(8\over 5\right)\)=1
\(\Rightarrow\ \ \ a={11\over5}-1={11\over 5}\)
Hence, \(a={11\over 5}, b={8\over 5}\)

-x+2y-7=0