Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ 2x – 3y + 13 = 0 \]

\[ 3x – 2y + 12 = 0 \]

Solution

Step 1: Write Both Equations in the Form \(y = mx + c\)

Equation (1):

\[ 2x – 3y + 13 = 0 \Rightarrow -3y = -2x – 13 \Rightarrow y = \frac{2x + 13}{3} \]

Equation (2):

\[ 3x – 2y + 12 = 0 \Rightarrow -2y = -3x – 12 \Rightarrow y = \frac{3x + 12}{2} \]

Step 2: Prepare Table of Values

For Equation (1): \(2x – 3y + 13 = 0\)

x	y
-5	1
-2	3

For Equation (2): \(3x – 2y + 12 = 0\)

x	y
-4	0
-2	3

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

• Line 1: (−5, 1) and (−2, 3)
• Line 2: (−4, 0) and (−2, 3)

Join each pair of points to obtain two straight lines.

The two lines intersect at the point:

\[ (-2,\,3) \]

Conclusion

The graphical solution of the given system of equations is:

\[ \boxed{x = -2,\; y = 3} \]

Hence, the two lines intersect at the point (−2, 3).