Finding Solutions of Linear Equations in Two Variables
Finding Solutions of Linear Equations in Two Variables
Let 
, where a, b, c are real numbers such that 
and 
. Then, any pair of values of x and y which satisfies the equation , is called a solution of it.
Consider the equation 3x-2y=5. We observe that x= 3, y=2 is a solution of 3x-2y=5 because when we substitute the value of x and y
we have:
But, x=3, y= -2 is not its solution, because
i.e. when x= 3 and y = -2.
Illustration: Show that (x=1, y=1) as well as (x=2,y=5) is a solution of 4x-y-3=0
Solution: If we put x=1 and y=1 in the given equation, we have
So, (x=1, y=1) is a solution of 4x-y-3=0
If we put (x=2, y=5) in the equation 4x-y-3=0 we have
So, (x=2, y=5) is a solution of 4x-y-3=0.
So we can say that a linear equation can have more than one solution. In fact, we can find as many solutions as we require. To find solution of a linear equation we can substitute a value of our choice for one variable say x and can then find the value of y.
For Example Let x =0 in 4x-y-3=0
The equation reduces to
So,(0,-3) is another solution of 4x-y-3=0.
Thus, a linear equation in two variables has infinitely many solutions.
Which of the following ordered pairs represents a solution for the linear equation 3x - 2y = 2 ? | |||
| Right Option : B | |||
| View Explanation | |||
Which of the following ordered pair represents a solution for the linear equation ? | |||
| Right Option : C | |||
| View Explanation | |||
Which of the following ordered pair represents a solution for the linear equation 3x + 4y = -6? | |||
| Right Option : D | |||
| View Explanation | |||
Students / Parents Reviews [20]
Abhyas 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
10thMy 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
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
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Barkha Arora
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Manish Kumar
10thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
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8thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
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Archit Segal
7thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
10thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
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Eshan Arora
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
Anika Saxena
8thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thAbhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of performance in Abhyas exams. He is satisfied with institute.
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7thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thBeing 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.
