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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

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#### 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.

2*x* + *y* − 6 = 0

*y* = 6 − 2*x*

x | 0 | 1 | 2 |

y | 6 | 4 | 2 |

And 4*x *− 2*y* − 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.

Concept: Graphical Method of Solution of a Pair of Linear Equations

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