Solve the system of equations graphically:
2x-3y+13=0
3x-2y+12=0
Solve the system of equations graphically:
2x-3y+13=0
3x-2y+12=0

Solution:

From the first eq., write y in terms of x
y=\frac{2 x+13}{3}\dots \dots (i)
Substituting different values of x in eq.(i) to get different values of y
For x=-5, y=\frac{-10+13}{3}=1
For x=1, y=\frac{2+13}{3}=5
For x=4, y=\frac{8+13}{3}=7

Therefore, the table for the first eq. (2 x-3 y+13=0 ) is

    \[\begin{tabular}{|r|r|r|r|} \hline $\mathrm{x}$ & $-5$ & 1 & 4 \\ \hline $\mathrm{y}$ & 1 & 5 & 7 \\ \hline \end{tabular}\]

Now, plot the points \mathrm{A}(-5,1), \mathrm{B}(1,5) and \mathrm{C}(4,7) on a graph paper and join \mathrm{A}, \mathrm{B} and \mathrm{C} to get the graph of 2 \mathrm{x}-3 \mathrm{y}+13=0

From the second eq., write y in terms of x
y=\frac{3 x+12}{2}\dots \dots(ii)
Substituting different values of x in eq.(ii) to get different values of y
For x=-4, y=\frac{-12+12}{2}=0
For x=-2, y=\frac{-6+12}{2}=3
For x=0, y=\frac{0+12}{2}=6
Therefore, the table for the second equation (3 x-2 y+12=0) is

    \[\begin{tabular}{|r|c|c|r|} \hline $\mathrm{x}$ & $-4$ & $-2$ & 0 \\ \hline $\mathrm{y}$ & 0 & 3 & 6 \\ \hline \end{tabular}\]

Now, plot the points \mathrm{D}(-4,0), \mathrm{E}(-2,3) and \mathrm{F}(0,6) on the same graph paper and join \mathrm{D}, \mathrm{E} and \mathrm{F} to get the graph of 3 \mathrm{x}-2 \mathrm{y}+12=0.

It is clear from the graph that, the given lines intersect at (-2,3).
Hence, the solution of the given system of equation is (-2,3).