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Solution - Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: 2x + y – 6 = 0, 4x – 2y – 4 = 0 - CBSE Class 10 - Mathematics

ConceptGraphical Method of Solution of a Pair of Linear Equations

Question

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: 2x + y – 6 = 0, 4x – 2y – 4 = 0

Solution

2x + y - 6 = 0

4x - 2y - 4 = 0

`a_1/a_2 = 2/4 = 1/2, b_1/b_2 = (-1)/2 and c_1/c_2 = (-6)/-4 = 3/2`

Since `a_1/a_2 != b_1/b_2`

Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

2x + y − 6 = 0

y = 6 − 2x

x 0 1 2
y 6 4 2

And 4− 2y − 4 = 0

`y = (4x - 4)/2`

x 1 2 3
y 0 2 4

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines are intersecting each other at the only point i.e., (2, 2) and it is the solution for the given pair of equations.

Is there an error in this question or solution?

APPEARS IN

NCERT Mathematics Textbook for Class 10
Chapter 3: Pair of Linear Equations in Two Variables
Q: 4.3 | Page no. 50

Reference Material

Solution for question: Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: 2x + y – 6 = 0, 4x – 2y – 4 = 0 concept: Graphical Method of Solution of a Pair of Linear Equations. For the course CBSE
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