MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesWrite the condition under which a pair of linear equations has no solution. What type of lines do they represent graphically?

For a pair of linear equations $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$, the condition for having no solution is: $$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$ \nGraphical Representation: Under this condition, the two straight lines represented by the given linear equations are completely parallel to each other on the Cartesian plane. Because parallel lines never intersect at any point, there exists no common ordered pair $(x, y)$ that satisfies both equations simultaneously. Therefore, the system of equations has no solution and is termed as inconsistent.