Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

 

ii) x –(y/5)–10 = 0

Solution:

The equation x –(y/5)-10 = 0 can be written as,

1x+(-1/5)y +(–10) = 0

Now comparing x+(-1/5)y+(–10) = 0 with ax+by+c = 0

We get,

a = 1

b = -(1/5)

c = -10

(iii) –2x+3y = 6

Solution:

–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

(iv) x = 3y

Solution:

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

(v) 2x = –5y

Solution:

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

(vi) 3x+2 = 0

Solution:

3x+2 = 0

The equation 3x+2 = 0 can be written as,

3x+0y+2 = 0

Now comparing 3x+0+2= 0 with ax+by+c = 0

We get, a = 3

b = 0

c = 2

(vii) y–2 = 0

Solution:

y–2 = 0

The equation y–2 = 0 can be written as,

0x+1y+(–2) = 0

Now comparing 0x+1y+(–2) = 0with ax+by+c = 0

We get, a = 0

b = 1

c = –2

(viii) 5 = 2x

Solution:

5 = 2x

Re-arranging the equation, we get,

2x = 5

i.e., 2x–5 = 0

The equation 2x–5 = 0 can be written as,

2x+0y–5 = 0

Now comparing 2x+0y–5 = 0 with ax+by+c = 0

We get, a = 2

b = 0

c = -5