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Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: x + y = 5, 2x + 2y = 10 - CBSE Class 10 - Mathematics

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Question

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: x + y = 5, 2x + 2y = 10

Solution

x + y = 5

2x + 2y = 10

`a_1/a_2=1/2, b_1/b_2=1/2, c_1/c_2 = 5/10 =1/2`

Since `a_1/a_2=b_1/b_2=c_1/c_2`

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

x + y = 5

x = 5 - y

x 4 3 2
y 1 2 3

And, 2x + 2y = 10

`x =(10-2y)/2`

x 4 3 2
y 1 2 3

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines are overlapping each other. Therefore, infinite solutions are possible for the given pair of equations

  Is there an error in this question or solution?

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 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 3: Pair of Linear Equations in Two Variables
Ex. 3.20 | Q: 4.1 | Page no. 50
Solution Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: x + y = 5, 2x + 2y = 10 Concept: Graphical Method of Solution of a Pair of Linear Equations.
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