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

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#### 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

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

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