Question

The pair of linear equations $5x+4y=20$ and $10x+8y=16$, will have

• A. no solution
• B. many solutions
• C. two solutions
• D. one solution

Answer 1

The correct option is A no solution

For the given pair of equations $5x+4y=20$ and $10x+8y=16$;

$\frac{a_1}{a_2}=\frac{5}{10}=\frac{1}{2}$

$\frac{b_1}{c_2}=\frac{4}{8}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-20}{-16}=\frac{5}{4}$

As the given pair of linear equation satisfies -

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

The graph will be a pair of parallel lines and so the pair of equations will have no solution.