Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ x + y = 4 \]

\[ 2x – 3y = 3 \]

Solution

Step 1: Write Both Equations in a Convenient Form

Equation (1):

\[ x + y = 4 \Rightarrow y = 4 – x \]

Equation (2):

\[ 2x – 3y = 3 \Rightarrow 3y = 2x – 3 \Rightarrow y = \frac{2x – 3}{3} \]

Step 2: Prepare Table of Values

For Equation (1): \(x + y = 4\)

x	y
0	4
4	0

For Equation (2): \(2x – 3y = 3\)

x	y
3	1
0	-1

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

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

Join each pair of points to obtain two straight lines.

The two lines intersect at the point:

\[ (3,\,1) \]

Conclusion

The graphical solution of the given system of equations is:

\[ \boxed{x = 3,\; y = 1} \]

Hence, the two lines intersect at the point (3, 1).