**Pair of Linear Equations In Two Variables**

**Solved Examples**

**Q1: Solve the following system of linear equations by elimination method (equating the coefficients).**

**6 (ax + by) = 3a + 2b**

**6 (bx – ay) = 3b – 2a**

Answer:

Given equations :

6 (ax + by) = 3a + 2b ...(1)

6 (bx – ay) = 3b – 2a ...(2)

multiply eqn. (1) by a and equation (2) by b, and add, we get

6a²x + 6aby = 3a² + 2ab

6b²x – 6aby = 3b² – 2ab

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6 (a² + b²)x = 3(a + b)

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⇒ x = ½

Put x = ½ in equation (1), we have

6a × ½ + 6by = 3a + 2b

6by = 2b

⇒ y = ⅓

∴ x = ½ and y = ⅓ (

**Answer**)

**Q2: 2 tables and 3 chairs together cost Rs. 2000 whereas 3 tables and 2 chairs together cost ₹2500. Find the total cost of 1 table and 5 chairs.**

Answer: Let the cost of a table be Rs. x and that of a chair be Rs. y.

According to given question,

2x + 3y = 2000 ...(1)

3x + 2y = 2500 ...(2)

Adding eqn. (1) and (2), we get

5x + 5y = 4500

⇒ x + y = 900 ...(3)

Subtracting eqn. (1) from eqn. (2), we get

x – y = 500 ...(4)

Adding eqn. (3) and eqn. (4), we get

2x = 1400

⇒ x = 700

Using x = 700 in eqn. (3), we get

700 + y = 900

⇒ y = 200

∴ Cost of 1 table = ₹ 700 and cost of 1 chair = ₹ 200.

Hence, cost of 1 table and 5 chairs = (x + 5y) = ₹ 700 + 5 (200) = ₹ 1700 (

**Answer**)

**Q3: Two angles are supplementary The larger angle is 3° less than twice the measure of the smaller angle. Find the measure of each angle.**

Answer: Let the larger supplementary angle = x°

Smaller supplementary angle = y°

According to the question,

x = 2y – 3 ... (1)

Sum of the supplementary angles is 180°

x + y = 180 ... (2)

Subtract eqn. (1) from eqn. (2), we get

x + y = 180

x – 2y = -3

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3y = 183

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⇒ y = 61

Substitute the value of y in (1) or (2)

x + y = 180

x + 61 = 180

⇒ x = 119°

∴ Two angles are 119° and 61°. (

**Answer**)

**Q4: 5 books and 7 pens together cost ₹79 whereas 7 books and 5 pens together cost ₹ 77. Find the total cost of 1 book and 2 pens.**

Answer:

Let the cost of a book be ₹ x and that of a pen be ₹ y. Then,

5x + 7y = 79 ..... (1)

and,

7x + 5y = 77 .... (2)

Multiply equation (1) by 5 and equation (2) by 7, we get

25x + 35y = 395 ...... (3)

49x + 35y = 539 .......(4)

Subtracting equation (3) by equation (4), we get

49x - 25x = 539 - 395

⇒ 24x = 144

⇒ x = 6

∴ Cost of a book = ₹ 6

Put x = 6 in equation (1), we get

5 × 6 + 7y = 79

⇒ 30 + 7y = 79

⇒ 7y = 79 - 30

⇒ 7y = 49

⇒ y = 7

∴ Cost of a pen ₹ 7

∴ Cost of 2 pens = 2 × 7 = ₹ 14

Hence, the total cost of 1 book and 2 pens = 6 + 14 = ₹ 20 (

**Answer**)

**☛See also:**

CH 2: Polynomials (Study Points)

CH 2: Polynomials (NCERT Ex 2.1)

CH 2: Polynomials (NCERT Ex 2.2)

CH 3: Linear Equations In Two Variables (Revision Assignment)

CH 3: Linear Equations In Two Variables (Solved Examples)

CH 4 : Quadratic Equations (Ex 4.1)

CH 4 : Quadratic Equations (NCERT Ex 4.2)

CH 4: Quadratic Equations (Summary)

CH 5: Arithmetic Progressions (MCQs)

CH5: Arithmetic Progressions - Seven Problems You Must Know

CH5: Arithmetic Progressions (Q & A)