Finding Solutions of Linear Equations in Two Variables


 
 
Concept Explanation
 

Finding Solutions of Linear Equations in Two Variables

 Let ax+by+c=0, where a, b, c are real numbers such that aneq 0  and  bneq 0. Then, any pair of values of x and y which satisfies the equation ax+by+c=0, 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: LHS = 3times 3-2times 2=5=RHS.

But, x=3, y= -2 is not its solution, because

large L.H.S=3times 3-2times(- 2)=9+4=13 neq 5

i.e. LHSneq RHS 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

                      LHS=4times 1-1-3=0=RHS

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

                    LHS=4times 2-5-3=0=RHS

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 4times 0-y-3=0Rightarrow -y=3Rightarrow y=-3

So,(0,-3) is another solution of 4x-y-3=0.

Thus, a linear equation in two variables has infinitely many solutions.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

In the linear equation 3x - 4y = 7, If x = 5 then the value of 'y' is  ________________

Right Option : D
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Question : 2

A pair of linear equations which has a unique solution x=2,y=-3 is

Right Option : D
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Explanation
Question : 3

Find the value of a for which the equation 2 x + a y = 5 has (1, -1) as a solution. Find two more solutions for the equation obtained

Right Option : A
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Explanation
 
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