Step 1: Table of solutions for $2x + 3y = 5$, i.e. $y = \dfrac{5 - 2x}{3}$.

| $x$ | 1 | 4 | -2 |
|---|---|---|---|
| $y$ | 1 | -1 | 3 |

Step 2: Table of solutions for $-3x + y = -2$, i.e. $y = 3x - 2$.

| $x$ | 0 | 1 | 2 |
|---|---|---|---|
| $y$ | -2 | 1 | 4 |

Step 3: Plot both sets of points on the same graph paper and join to get two straight lines.
Step 4: The two lines intersect at the point $(1, 1)$.
Step 5: Hence the solution is $$x = 1,\qquad y = 1$$
Verification :
$$2(1) + 3(1) = 5 \ \checkmark$$
$$-3(1) + 1 = -2 \ \checkmark$$