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 x - y = 4, if y = 2, the value of 'x' is ________________ | |||
| Right Option : D | |||
| View Explanation | |||
In the linear equation | |||
| Right Option : B | |||
| View Explanation | |||
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