Question

Find the value of alpha and beta for which the following pair of linear equations has

infinite number of solutions:

2x + 3y = 7;

αx + (α + β)y = 28​

Answer 1

Answer:

$\alpha = 4 \\ \beta = 2$

Step-by-step explanation:

$\: \: \: \: 2x + 3y = 7 \\ \: \: \alpha \: x + ( \alpha + \beta )y = 28 \\ \div 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \frac{ \alpha x + ( \alpha + \beta )y}{4} = 7 \\ \frac{ \alpha x + ( \alpha + \beta )y}{4} = 2x + 3y \\ \alpha x + ( \alpha + \beta )y = 4x + 6y$

On comparing with

$\alpha = 4 \\ \alpha + \beta = 6 \\ now \: \: \: \: \: \: \: \: \: \\ 4 + \beta = 6 \\ \beta = 2 \\ result. \\ \alpha = 4 \\ \beta = 2$