## Linear Equations In Two Variables

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Q1: The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

Answer:

Let the cost of a notebook and a pen be x and y respectively.

Cost of notebook = 2 ☓ Cost of pen

x = 2y

x − 2y = 0

**Q2: Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case:**

(i) 2x + 3y = 9.35

(i) 2x + 3y = 9.35

(ii) x - y/5 - 10 = 0

(iii) − 2x + 3 y = 6

(iv) x = 3y

(v) 2x = − 5y

(vi) 3x + 2 = 0

(vii) y − 2 = 0

(viii) 5 = 2x

(ii) x - y/5 - 10 = 0

(iii) − 2x + 3 y = 6

(iv) x = 3y

(v) 2x = − 5y

(vi) 3x + 2 = 0

(vii) y − 2 = 0

(viii) 5 = 2x

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Answer:

**(i) ****2x + 3y = 9.3****5**

2x + 3y - 9.35 = 0

Comparing this equation with ax + by + c = 0,

a = 2, b = 3, c = - 9.35

**(ii) ****x - y/5 - 10 = 0**

Comparing this equation with ax + by + c = 0,

a = 1, b =-1/5 , c = −10

(iii) **− 2x + 3 y =** **6**

− 2x + 3 y − 6 = 0

Comparing this equation with ax + by + c = 0,

a = −2, b = 3, c = −6

(iv) **x = 3y**

1x − 3y + 0 = 0

Comparing this equation with ax + by + c = 0,

a = 1, b = −3, c = 0

(v) **2x = −5y**

2x + 5y + 0 = 0

Comparing this equation with ax + by + c = 0,

a = 2, b = 5, c = 0

(vi) **3x + 2 = 0**

3x + 0.y + 2 = 0

Comparing this equation with ax + by + c = 0,

a = 3, b = 0, c = 2

(vii) **y − 2 = 0**

0.x + 1.y − 2 = 0

Comparing this equation with ax + by + c = 0,

a = 0, b = 1, c = −2

(viii)**5 = 2x**

− 2x + 0.y + 5 = 0

Comparing this equation with ax + by + c = 0,

a = −2, b = 0, c = 5

**2x + 3y = 9.3**

**5**

**x - y/5 - 10 = 0**

very nice very helpful for understanding

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