**Linear Equations in Two Variables – Maharashtra Board Class 9 Solutions for Algebra**

AlgebraGeometryScience and TechnologyHindi

**Exercise – 4.1**

**Solution 1:**

- 2x + 5y = 7; x – 10y = 11; 4x + 9y = 13
- No. The given equation is not of the type ax + by = c, hence it is not a linear equation.
- P is a real number. P > 0.
- (1, 17), (2, 16), etc. There are infinite solutions.
- Substituting x = 1 and y = a in the equation x + 3y = 10, we get,1 + 3a = 10

∴3a = 10 – 1

∴3a = 9

∴ a = 3

**Solution 2(i):**

**Solution 2(ii):**

**Solution 2(iii):**

**Solution 2(iv):**

**Solution 2(v):**

**Exercise – 4.2**

**Solution 1(i):**

2x + 3y = -4 …(i)

x – 5y = 11 …(ii)

From equation (ii), we can express x in terms of y,

∴ x = 5y + 11 …(iii)

Substitute this value of x in equation (i)

∴ 2(5y + 11) + 3y = -4

∴ 10y + 22 + 3y = -4

∴ 13y +22 = -4

∴ 13y = -4 – 22

∴ 13y = -26

∴ y = -2

Substituting y = -2 in equation (iii),

x = 5(-2) + 11

∴ x = -10 + 11

∴ x = 1

∴ x = 1 and y = -2

**Solution 1(ii):**

x + 2y = 0 …(i)

10x + 15y = 105 …(ii)

Dividing both sides of equation (ii) by 5, we get

2x + 3y = 21 …(iii)

Expressing x in terms of y in equation (i)

x = 2y …(iv)

Substitute x = 2y in equation (iii)

∴ 2(2y) + 3y = 21

∴ 4y + 3y = 21

∴ 7y = 21

∴ y = 3

Substituting y = 3 in equation (iii),

x = 2(3)

∴ x = 6

∴ x = 6 and y = 3

**Solution 1(iii):**

**Solution 1(iv):**

**Solution 1(v):**

2x – y – 3 = 0 …(i)

4x – y – 5 = 0 …(ii)

∴ 2x – y – 3 = 0

∴ y = 2x – 3 …(iii)

Substitute y = 2x – 3 in equation (ii),

∴ 4x – (2x – 3) – 5 = 0

∴ 4x – 2x + 3 – 5 = 0

∴ 2x = 5 – 3

∴ 2x = 2

∴ x = 1

Put x = 1 in equation (iii),

y = 2(1) – 3

∴ y = 2 – 3

∴ y = -1

∴ x = 1 and y = -1

**Solution 1(vi):**

**Exercise – 4.3**

**Solution 1(i):**

**Solution 1(ii):**

**Solution 1(iii):**

**Solution 1(iv):**

**Solution 2(i):**

**Solution 2(ii):**

**Solution 2(iii):**

**Solution 2(iv):**

**Solution 2(v):**

**Exercise – 4.3**

**Solution 1(i):**

Let the two numbers be x and y. x > y

According to the first condition,

x + y = 125 …(i)

According to the second condition,

x – y = 25 …(ii)

**Solution 1(ii):**

Let the complementary angles be x and y. x > y

So, x + y = 90° (∵Sum of complementary angles is 90°)

According to the given condition,

x – y = 6°

**Solution 1(iii):**

Let the length of the rectangle be x cm and the breadth be y cm.

According to the first condition,

x = y + 4

x – y = 4 …(i)

According to the second condition,

2(x + y) = 40

x + y = 20 …(ii)

**Solution 1(iv):**

Let Sonali’s age be x years and Monali’s age of y years.

According to the first condition,

x + y = 29 …(i)

According to the second condition,

y = x – 3

x – y = 3 …(ii)

**Solution 1(v):**

Let the father’s age be x years and the son’s age be y years.

According to the first condition,

x = 4y

x – 4y = 0 …(i)

According to the second condition,

x – y = 30 …(ii)

**Solution 2(i):**

**Solution 2(ii):**

**Solution 2(iii):**

**Solution 2(iv):**

**Solution 2(v):**

**Solution 2(vi):**