Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:

x – y = 8, 3x – 3y = 16

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#### Solution

x - y = 8

3x - 3y = 16

`a_1/a_2 = 1/3, b_1/b_2 = (-1)/-3 = 1/3 and c_1/c_2 = 8/16 = 1/2`

Since `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Therefore, these linear equations are parallel to each other and thus have no possible solution. Hence, the pair of linear equations is inconsistent.

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

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