Question
Is the pair of linear equation consistent/inconsistent? If consistent, obtain the solution graphically: 2x – 2y – 2 = 0; 4x – 4y – 5 = 0
✓
Answer
2 x - 2 x - 2 = 0................(1)
4 x - 4 y - 5 = 0..................(2)
Here, $a _ { 1 } = 2 , \quad b = - 2 , c _ { 1 } = - 2$
$a _ { 2 } = 4 , b _ { 2 } = - 4 , c _ { 2 } = - 5$
We see that $\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } \neq \frac { c _ { 1 } } { c _ { 2 } }$
Hence, the lines represented by the equations(1) and ( 2 ) are parallel.
Therefore, equations ( 1) and (2) have no solution, i.e., the given pair of a linear equation is inconsistent.
4 x - 4 y - 5 = 0..................(2)
Here, $a _ { 1 } = 2 , \quad b = - 2 , c _ { 1 } = - 2$
$a _ { 2 } = 4 , b _ { 2 } = - 4 , c _ { 2 } = - 5$
We see that $\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } \neq \frac { c _ { 1 } } { c _ { 2 } }$
Hence, the lines represented by the equations(1) and ( 2 ) are parallel.
Therefore, equations ( 1) and (2) have no solution, i.e., the given pair of a linear equation is inconsistent.
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