# 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

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Fraction as a Part of Collection | Pictures of Fraction | Fractional

Feb 24, 24 04:33 PM

How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

2. ### Fraction of a Whole Numbers | Fractional Number |Examples with Picture

Feb 24, 24 04:11 PM

Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

3. ### Identification of the Parts of a Fraction | Fractional Numbers | Parts

Feb 24, 24 04:10 PM

We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

4. ### Numerator and Denominator of a Fraction | Numerator of the Fraction

Feb 24, 24 04:09 PM

What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.