Question

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 = 9.35

(ii) x – $\frac{y}{5}$– 10 = 0

(iii) –2x + 3y = 6

(iv) x = 3y

(v) 2x = –5y

(vi) 3x + 2 = 0

(vii) y – 2 = 0

Answer 1

(i) 2x+3y=9.35
⇒ 2x+3y−9.35=0
On comparing this equation with ax+by+c=0,
a=2,b=3 and c=−9.35

(ii) x−$\frac{y}{5}$−10=0
On comparing this equation with ax+by+c=0,
a=1,b=−$\frac{1}{5}$ and c=−10
(iii) −2x+3y=6
⇒ −2x+3y−6=0
On comparing this equation with ax+by+c=0,
a=−2,b=3 and c=−6
(iv) x=3y
⇒ x−3y=0
On comparing this equation with ax+by+c=0, we get,
a=1,b=−3 and c=0
(v) 2x=−5y
⇒ 2x+5y=0
On comparing this equation with ax+by+c=0,
a=2,b=5 and c=0
(vi) 3x+2=0
⇒ 3x+0y+2=0
On comparing this equation with ax+by+c=0,
a=3,b=0 and c=2
(vii) y−2=0
⇒ 0x+y−2=0
On comparing this equation with ax+by+c=0,
a=0,b=1 and c=−2
(viii) 5=2x
⇒ −2x+0y+5=0
On comparing this equation with ax+by+c=0,
a=−2,b=0 and c=5