Find the values of a and b for which the system of linear equations

Find the values of a and b for which the system of linear equations 3x + 4y = 12, (a + b)x + 2(a - b)y = 24 has infinite number of solutions.

Answer

For Infinite number of solutions,

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

$$ \frac{3}{a + b} = \frac{4}{2(a-b)} = \frac{12}{24} $$

$$ \frac{3}{a + b} = \frac{1}{2} \Rightarrow a + b = 6 $$

$$ \frac{2}{a - b} = \frac{1}{2} \Rightarrow a - b = 4 $$

On solving, a = 5, b = 1