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 y - 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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