Express the following linear equations in the form ax + by + c = 0 and

1.	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 = 12(ii) x – y/2 – 5 = 0(iii) 2x + 3y = 9.35(iv) 3x = -7y (v) 2x + 3 = 0 (vi) y – 5 = 0 (vii) 4 = 3x (viii) y = x/2
Answer» (i) Given equation, -2x + 3y = 12 Or – 2x + 3y – 12 = 0 Comparing the given equation with ax + by + c = 0 We get, a = – 2; b = 3; c = -12 (ii) Given equation, x – y/2 – 5 = 0 Comparing the given equation with ax + by + c = 0, We get, a = 1; b = -1/2, c = -5 (iii) Given equation, 2x + 3y = 9.35 or 2x + 3y – 9.35 = 0 Comparing the given equation with ax + by + c = 0 We get, a = 2 ; b = 3 ; c = -9.35 (iv) Given equation, 3x = -7y or 3x + 7y = 0 Comparing the given equation with ax+ by + c = 0, We get, a = 3 ; b = 7 ; c = 0 (v) Given equation, 2x + 3 = 0 or 2x + 0y + 3 = 0 Comparing the given equation with ax + by + c = 0, We get, a = 2 ; b = 0 ; c = 3 (vi) Given equation, y – 5 = 0 or 0x + y – 5 = 0 Comparing the given equation with ax + by+ c = 0, We get, a = 0; b = 1; c = -5 (vii) Given equation, 4 = 3x or 3x + 0y – 4 = 0 Comparing the given equation with ax + by + c = 0, We get, a = 3; b = 0; c = -4 (viii) Given equation, y = x/2 Or x – 2y = 0 Or x – 2y + 0 = 0 Comparing the given equation with ax + by + c = 0, We get, a = 1; b = -2; c = 0

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 = 12(ii) x – y/2 – 5 = 0(iii) 2x + 3y = 9.35(iv) 3x = -7y (v) 2x + 3 = 0 (vi) y – 5 = 0 (vii) 4 = 3x (viii) y = x/2

Answer»

(i) Given equation, -2x + 3y = 12

Or – 2x + 3y – 12 = 0

Comparing the given equation with ax + by + c = 0

We get, a = – 2; b = 3; c = -12

(ii) Given equation, x – y/2 – 5 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 1; b = -1/2, c = -5

(iii) Given equation, 2x + 3y = 9.35

or 2x + 3y – 9.35 = 0

Comparing the given equation with ax + by + c = 0

We get, a = 2 ; b = 3 ; c = -9.35

(iv) Given equation, 3x = -7y

or 3x + 7y = 0

Comparing the given equation with ax+ by + c = 0,

We get, a = 3 ; b = 7 ; c = 0

(v) Given equation, 2x + 3 = 0

or 2x + 0y + 3 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 2 ; b = 0 ; c = 3

(vi) Given equation, y – 5 = 0

or 0x + y – 5 = 0

Comparing the given equation with ax + by+ c = 0,

We get, a = 0; b = 1; c = -5

(vii) Given equation, 4 = 3x

or 3x + 0y – 4 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 3; b = 0; c = -4

(viii) Given equation, y = x/2

Or x – 2y = 0

Or x – 2y + 0 = 0

Comparing the given equation with ax + by + c = 0,

We get, a = 1; b = -2; c = 0