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Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i) x + y = 5, 2x + 2y = 10 (ii) x – y = 8, 3x – 3y = 16 (iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0 (iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
Asked by Akhil Last Modified
Answer 
Tasneem
Here,
,
Thus, the pair of linear equations is consistent.
Now, x + y = 5 
x = 5 - y
| x | 4 | 3 | 2 |
| y | 1 | 2 | 3 |
| x | 4 | 3 | 2 |
| y | 1 | 2 | 3 |
From the graph, it can be observed that the two lines coincide. Thus, the given pair of equations has infinite solutions.
Let x = k, then y = 5 - k. So, the ordered pair (k, 5 - k) , where k is a constant, will be the solution of the given pair of linear equations.
Here,
Thus, the pair of linear equations is inconsistent. Hence the lines appear parallel.
since , the equation has only one solution.
Thus, the pair of linear equations is consistent.
Now, 2x + y - 6 = 0 y = 6 - 2x
| x | 0 | 1 | 2 |
| y | 6 | 4 | 2 |
| x | 1 | 2 | 3 |
| y | 0 | 2 | 4 |
From the graph, it can be observed that the two lines intersect each other at the point (2, 2). Thus, the solution of the given pair of equations is (2, 2).
The equation has no solution.
Thus, the pair of linear equations is inconsistent.
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