Question

Find the value of $\alpha$ and $\beta$ for which the following system of linear equations has infinite number of solutions:
$2x+3y=7;2\alpha x+(\alpha +\beta )y=28$

Answer 1

For infinite number of solutions

$\frac{2}{2\alpha }=\frac{3}{\alpha +\beta }=\frac{7}{28}$

$\frac{2}{2\alpha }=\frac{7}{28}$

$\alpha =4$

$\frac{3}{\alpha +\beta }=\frac{7}{28}$

$\frac{3}{4+\beta }=\frac{1}{4}$

$4+\beta =12$

$\beta =8$