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












8th Grade Math Practice 

From Pairs of Equations to HOME PAGE




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.



New! Comments

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

Share this page: What’s this?



Recent Articles

  1. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 18, 24 02:59 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More

  2. Numbers | Notation | Numeration | Numeral | Estimation | Examples

    May 12, 24 06:28 PM

    Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects

    Read More

  3. Face Value and Place Value|Difference Between Place Value & Face Value

    May 12, 24 06:23 PM

    Face Value and Place Value
    What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

    Read More

  4. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    May 12, 24 06:09 PM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  5. Worksheet on Bar Graphs | Bar Graphs or Column Graphs | Graphing Bar

    May 12, 24 04:59 PM

    Bar Graph Worksheet
    In math worksheet on bar graphs students can practice the questions on how to make and read bar graphs or column graphs. Test your knowledge by practicing this graphing worksheet where we will

    Read More