**Solution Of A Linear Equation In Two Variables Example Problems With Solutions**

**Method:** Put the value of x (or y) = 0, ±1, ±2, ±3,……, we get values of y (or x). By this we can find many solutions of given equation.

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**Example 1:** Find five solutions of

(i) 2x + 3y = 6 (ii) 3x – 2y = 12 (iii) 7x + y = 15

**Solution: **(i) 2x = 6 – 3y

**Example 2:** Find two solutions of

(i) 3x – 7y = 21 (ii) 8x – 5y = 16

**Solution: **(i) 3x – 7y = 21

**Example 3:** Find five solutions of

(i) 3x = 5 (ii) 7y = 10

**Solution: **(i) The equation is only in one variable. So we have to convert into 2 variable 3x + 0.y = 5

**Note:**

**Ordered Pair:** If value of x & y are represent in form (x, y) then this form is called ordered pair form : Eg. x = 5, y = 7/3 then ordered pair form = (5, 7/3). First part is called abscissa (x part) and second part is ordinate (y part).

**Example 4: ** Check the following value of x & y are solution of equation 9x – 8y = 72 or not

(i) (0, 9) (ii) (0, – 9) (iii) (– 8, 0)

(iv) (+8, 0) (v) (1, 1) (vi) (1/3, 1/2)

**Solution: **Given equation 9x – 8y = 72

**Example 5: **Find the value of k in equation 2x + ky = 6 if (–2, 2) is a solution.

**Solution: **∵ (–2, 2) is a solution of 2x + ky = 5

∴ 2(–2) + k(2) = 6

– 4 + 2k = 6 ⇒ 2k = 6 + 4

k = 10/2 = 5

**Example 6: **Find value of p if (4, –4) is a solution of x – py = 8.

**Solution: **x – py = 8

4 – p (–4) = 8

4p = 8 – 4

4p = 4

p = 1

**Example 7: ** Find the value of a if (a, –3a) is a solution of 14x + 3y = 35.

**Solution: **Put x = a and y = –3a in given equation

14(a) + 3(–3a) = 35

14a – 9a = 35

5a = 35

a = 7