Solve the equations using graphical method:
$\begin{align}
  & x+y=3; \\
 & -3x+2y=1 \\
\end{align}$
(A). (1, -2)
(B). (-1, 2)
(C). (1, 2)
(D). (-1, -2)

Hint: Draw the equations given in the question on the graph paper and see where the two lines are intersecting. The point on which the two equations of lines are intersecting is the solution is the two given equations.

Complete step-by-step solution -
The two simultaneous equations given in the question are:
$\begin{align}
  & x+y=3; \\
 & -3x+2y=1 \\
\end{align}$
We have asked to solve these two equations graphically.
In the below figure, we have graphically shown the two equations given in the question.

In the above figure, you can see two equations:
 $\begin{align}
  & x+y=3; \\
 & -3x+2y=1 \\
\end{align}$
You can also see a point A (1, 2) where the two lines of equation intersect each other. This intersecting point is the solution of the given system of simultaneous equations.
Now, you might wonder why A (1, 2) is the solution of the system of two simultaneous equations?
The answer is this point A (1, 2) at the same time satisfies both the equations.
In the following, we are going to show that the point A (1, 2) satisfies both the equations.
Checking the point A (1, 2) satisfies the equation $x+y=3$ or not by plugging $x=1\text{ and }y=2$ in this equation.
$\begin{align}
  & 1+2=3 \\
 & \Rightarrow 3=3 \\
\end{align}$
Hence, the point A (1, 2) has satisfied the equation $x+y=3$.
Checking the point A (1, 2) satisfies the equation $-3x+2y=1$ or not by plugging $x=1\text{ and }y=2$ in this equation.
$\begin{align}
  & -3\left( 1 \right)+2\left( 2 \right)=1 \\
 & \Rightarrow -3+4=1 \\
 & \Rightarrow 1=1 \\
\end{align}$
Hence, the point A (1, 2) has satisfied the equation $-3x+2y=1$.
Hence, the correct option is (c).

Note: You might want to know how we have drawn these lines of the equation on the graph. So, below we are going to discuss how to draw the equation of a line on the graph.
First of all, we are going to learn how to draw $x+y=3$ on the graph paper.
In the equation $x+y=3$, put $x=0$ then you will get the point (0, 3) on the y-axis. For a point on the x-axis, put $y=0$ in the equation $x+y=3$ you will get the point (3, 0). Now, join these two points (0, 3) and (3, 0). Hence, you have drawn the equation of a line on the graph paper. We follow the same process for line $-3x+2y=1$ for drawing on graph paper.
In the below figure, we have shown this drawing on the graph.