If $x = 2\alpha + 1$ and $y = \alpha - 1$ is a solution of the equation $2x – 3y + 5 = 0$, find the value of $\alpha$.

Given:

$x = 2\alpha + 1$ and $y = \alpha - 1$ is a solution of the equation $2x – 3y + 5 = 0$.

To do:

We have to find the value of $\alpha$.

Solution:

If $(x, y)$ is a solution of the equation $ax+by+c =0$, then it satisfies the given equation.

Therefore,

$2(2\alpha + 1) -3(\alpha - 1)+5=0$

$4\alpha+2-3\alpha+3+5=0$

$\alpha=-10$

The value of $\alpha$ is $-10$.