Answer
$\begin{bmatrix}x_1 \\x_2\end{bmatrix}=\begin{bmatrix}\dfrac{-3}{2}t+\dfrac{5}{2} \\ t\end{bmatrix}$; $t$ refers to a real number.
Work Step by Step
Since we have $2x_1+3x_2=5$, this can be re-written as:
$x_1=\dfrac{-3}{2}x_2+\dfrac{5}{2}$
Suppose $x_2=t$
Then:
Our desired solution set is: $\begin{bmatrix}x_1 \\x_2\end{bmatrix}=\begin{bmatrix}\dfrac{-3}{2}t+\dfrac{5}{2} \\ t\end{bmatrix}$; $t$ refers to a real number.
