Solving pairs of equations, indicate the pair or pairs representing simultaneous linear equations (solvable).

**1. **From the following pairs of equations find the pair or pairs representing simultaneous equations:

(i) 7x – 3y = 5

2x + 5y = 1**Solution:**

7/2 ≠ -3/5, so the two equations represent simultaneous equations; in this case they have only one solution.

(ii) 2x + 3y = 7

6x + 9y = 11**Solution:**

2/6 = 3/9 ≠ 7/11

Not simultaneous equations.

(iii) 6x - 4y = 8

3x - 2y = 4

**Solution:**

6/3 = -4/-2 = 8/4

Simultaneous equations; have infinite solutions.

**2.** For which value of k, kx + y = 2 and x + ky = 1 are inconsistent?

**Solution:**

The two equations will be inconsistent if k/1 = 1/k ≠ 2/1 that means, k² = 1 or k = ±1

Therefore, the two given equations will be inconsistent if k = ±1

**3.** If solvable, solve the following pairs of equations:

(i) 3x – 2y = 1

3x + 2y = 5

**Solution:**

Here, comparing co-efficient of x and y, we get;

3/3 ≠ -2/2

Therefore, adding the two equations, we get the general solution as shown below:

6x = 6

or, x = 1

Putting x = 1 in the first equation we get:;

3 × 1 – 2y = 1

or, 3 - 2y = 1

or, 3 – 3 – 2y = 1 – 3

or, -2y = -2

or, y = 1

Therefore, the required solution: x = 1, y = 1

(ii) 3x – 2y = 1

6x – 4y = 8

**Solution:**

Here, comparing the co-efficient of x, y we get;

3/6 = -2/-4 ≠ 1/8

So, the two equations have no general solution.

(iii) 3x – 2y = 2

9x – 6y = 6

**Solution:**

Comparing co-efficient of x, y and the term free from x, y we get;

3/9 = -2/-6 = 2/6

Therefore, two equations are, in fact, same.

Assuming x = c in 3x – 2y = 2 we get;

y = (3c – 2)/2

Therefore, required solution: x = c

y = (3c – 2)/2 for any real value of c.

● **Simultaneous Linear Equations**

**Solvability of Linear Simultaneous Equations**

**Word Problems on Simultaneous Linear Equations**

**Word Problems on Simultaneous Linear Equations**

**Practice Test on Word Problems Involving Simultaneous Linear Equations**

● **Simultaneous Linear Equations - Worksheets**

**Worksheet on Simultaneous Linear Equations**

**Worksheet on Problems on Simultaneous Linear Equations**

**8th Grade Math Practice**** ****From Pairs of Equations to HOME PAGE**

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