Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) –2x + 3y = 6
(ii) x = 3y
(iii) 2x = –5y
(i) –2x + 3y = 6
–2x + 3y = 6
Re-arranging the equation, we get,
–2x + 3y – 6 = 0
The equation –2x + 3y – 6 = 0 can be written as,
(–2)x + 3y + (– 6) = 0
Now comparing (–2)x + 3y + (–6) = 0 with ax + by + c = 0
We get, a = –2
b = 3
c =6
(ii) x = 3y
x = 3y
Re-arranging the equation, we get,
x-3y = 0
The equation x-3y=0 can be written as,
1x+(-3)y+(0)c = 0
Now comparing 1x+(-3)y+(0)c = 0 with ax + by + c = 0
We get, a = 1
b = -3
c = 0
(iii) 2x = –5y
2x = –5y
Re-arranging the equation, we get,
2x+5y = 0
The equation 2x + 5y = 0 can be written as,
2x + 5y + 0 = 0
Now comparing 2x + 5y + 0 = 0 with ax + by + c = 0
We get, a = 2
b = 5
c = 0