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 4x - 3y = 1? | |||
| Right Option : A | |||
| View Explanation | |||
In the linear equation | |||
| Right Option : C | |||
| View Explanation | |||
In the linear equation | |||
| Right Option : D | |||
| View Explanation | |||
Students / Parents Reviews [10]
My 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
7thI 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
10thAbhyas 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
10thOne 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
10thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thIt 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
8thIt 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
Barkha Arora
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
8thIt 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
10thA 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.
