Question

For the pair of linear equations $5x+7y=12$ and $10x+14y=20$ the solution set is____

• A. Infinite set
• B. Empty set
• C. Unique solution
• D. None of the above

Answer 1

The correct option is B Empty set

$asratioofcoefficientofxandyaresame\left(\frac{5}{10}\right)=\left(\frac{1}{2}\right)and\left(\frac{7}{14}\right)=\left(\frac{1}{2}\right)but\left(\frac{12}{10}\right)=\left(\frac{3}{5}\right)so\left(\frac{5}{10}\right)=\left(\frac{7}{14}\right)\ne \left(\frac{3}{5}\right)hencethesetwoequationhavenosolution,henceemptyset$