# Linear Equations in Two Variables – Exercise 4.2 – (MATHEMATICS) – 9th Class

**Exercise 4.2**

**1. Which on of the following option is true, and why?**

y = 3x + 5 has

(i) a unique solution,

(ii) only two solutions,

(iii) infinitely many solutions.

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**Sol. –**(iii) As each linear equation in two variables has infinitely many solutions. Further, for every x there is a corresponding value of y and vice – versa.

**2. Write four solutions for each of the following equations:**

(i) 2x + y = 7

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Sol. –

Consider equation: 2x + y = 7 ⇒ y = 7 – 2x

Let x = 0, then y = 7. Solution is x = 0, y = 7

Let x = 1, then y = 5. Solution is x = 1, y = 5

Let x = 2, then y = 3. Solution is x = 2, y = 3

Let x = 3, then y = 1. Solution is x = 3, y = 1.

(ii) πx + y = 9

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Sol. –

Consider equation: πx + y = 9 ⇒ y = 9 – πx

Let x = 0, then y = 9. Solution is x = 0, y = 9

Let x = 1, then y = 9 – π .Solution is x = 1, y =9 – π

Let x = 2, then y = 9 – 2π. Solution is x = 2, y = 9 – 2π.

Let x = 3, then y = 9 – 3π Solution is x = 3, y =9 – 3π.

(iii) x = 4y,

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Sol. –

Consider equation: x = 4y.

Let y = 0, then x = 0. Solution is x = 0, y = 0

Let y = 1, then x = 4. Solution is x = 4, y = 1

Let y = – 1, then x = – 4. Solution is x = – 4, y = – 1

Let y = 2, then x = 8. Solution is x = 8, y = 2.

**3. Check which of the following are solutions of the equation it x – 2y = 4 and which are not:**

(i) (0, 2)

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Sol. – For (0,2) substituting x = 0, y = 2 in (A), we get 0 – 4 = 4 ⇒ – 4 = 4 , not true.

Hence, (0,2) is not a solution.

(ii) (2, 0)

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Sol. – For (2,0) substituting x = 2, y = 0 in (A), we get

2 – 0 = 4 ⇒ 2 = 4, not true.

Hence, (2,0) is not a solution.

(iii) (4, 0)

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Sol. –

For (4,0), substituting x = 4, y = 0 in (A), we get

4 – 0 = 4 ⇒ 4 = 4, true.

Hence, (4,0) is a solution.

(iv)

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Sol. –

For , substituting x = , y = 4 in (A), we get

– 8 = 4 ⇒ – 7 = 4, not true.

Hence, is not a solution.

(v) (1, 1)

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Sol. –

For (1, 1), substituting x = 1, y = 1 in (A), we get

1 – 2 = 4 ⇒ – 1 = 4, not true.

Hence, (1,1) is not a solution.

**4. Find the value of ℜ, if x = 2, y = 1 is a solution. of the equation 2x + 3y ,= ℜ.**

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**Sol.**If x = 2, y = 1 is a solution of the equation 2x + 3y = ℜ then

4 + 3 = ℜ ⇒ ℜ = 7