Question
Is the pair of linear equation consistent/inconsistent? If consistent, obtain the solution graphically: x – y = 8; 3x – 3y = 16
✓
Answer
x - y = 8.................(1)
3 x - 3 y = 16.............(2)
Here, $a _ { 1 } = 1 , b _ { 1 } = - 1 , c _ { 1 } = - 8$
$a _ { 2 } = 3 , b _ { 2 } = - 3 , c _ { 2 } = - 16$
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 linear equation is inconsistent.
3 x - 3 y = 16.............(2)
Here, $a _ { 1 } = 1 , b _ { 1 } = - 1 , c _ { 1 } = - 8$
$a _ { 2 } = 3 , b _ { 2 } = - 3 , c _ { 2 } = - 16$
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 linear equation is inconsistent.
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