# Pairs of Equations

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

Simultaneous Linear Equations

Comparison Method

Elimination Method

Substitution Method

Cross-Multiplication Method

Solvability of Linear Simultaneous Equations

Pairs of 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