Question

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

Answer 1

Given

$\begin{array}{c}x=2\alpha +1\\ y=\alpha -1\end{array}$

put the value of $x$ and $y$ in the given equation

$\begin{array}{c}2x+3y+5=0\\ 2\left(2\alpha +1\right)+3\left(\alpha -1\right)+5=0\\ 4\alpha +2+3\alpha -3+5=0\\ 7\alpha +4=0\\ \alpha =\frac{-4}{7}\end{array}$