Elimination Method
Elimination Method
ELIMINATION METHOD:
Algorithm to find the solution:
Step 1: If coefficients of one variable ( either x or y ) in both the equations are not equal, then first multiply both the equations by some suitable non-zero constants to make the coeffiecients of one variable ( either x or y ) numerically equal.
Step 2: Add or subtract one equation from the other so that one variable gets eliminated.If you get an equaton in one variable, go to Step 3.
If in step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions.
If in step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is the given system is inconsistent.
Step 3: Solve the equation in one variable (x or y) so obtained to get its value.
Step 4: Susbtitute this valur of variable (x or y) in either of the original equations to get the value of the other variable.
Example : The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.
SOLUTION :
Let the incoome of the two person be Rs. 9x and Rs. 7x and their expenditures be Rs. 4y and Rs. 3y respectively. Then the equations formed for the given situation are given by :
9x - 4y = 2000 ............(i)
and 7x - 3y = 2000 .............(ii)
Step 1: Multiply Equation (i) by 3 and Equation (ii) by 4 to make the coefficients of y equal. Then we get the equations:
27x - 12 y = 6000 .........(iii)
28x - 12y = 8000 .........(iv)
Step 2: Subtract Equation (iii) from Equation (iv) to eliminate y, because the coefficients of y are the same. So, we get
(28x - 27x) - (12y - 127) = 8000 - 6000
i.e., x = 2000
Step 3: Subtituting this value of x in (i), we get
9(2000) - 4y = 2000 i.e.., y = 4000
So, the solution of the equations: x = 2000, y = 4000. Therefore, the monthly incomes of the two persons are Rs. 18,000 and Rs. 14000, respectively.
Verification : 18000 : 14000 = 9 : 7.
Also, the ratio of their expenditures = 18000 - 2000 : 14000 - 2000 = 16000 : 12000 = 4 : 3
Find the value of x and y : | |||
| Right Option : B | |||
| View Explanation | |||
Find the solution of : | |||
| Right Option : B | |||
| View Explanation | |||
Aruna has only Re 1 and Rs 2 coin with her. If the total number of coin that she has is 50 and the amount of money with her Rs 75 , then the number of Re 1 and Rs 2 coin are,respectively . | |||
| Right Option : D | |||
| View Explanation | |||
Students / Parents Reviews [10]
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
