Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ 2x + 3y = 4 \]

\[ x – y + 3 = 0 \]

Solution

Step 1: Write Both Equations in a Convenient Form

Equation (1):

\[ 2x + 3y = 4 \Rightarrow 3y = 4 – 2x \Rightarrow y = \frac{4 – 2x}{3} \]

Equation (2):

\[ x – y + 3 = 0 \Rightarrow y = x + 3 \]

Step 2: Prepare Table of Values

For Equation (1): \(2x + 3y = 4\)

x	y
2	0
-1	2

For Equation (2): \(x – y + 3 = 0\)

x	y
0	3
-1	2

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

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

Join each pair of points to obtain two straight lines.

The two lines intersect at the point:

\[ (-1,\,2) \]

Conclusion

The graphical solution of the given system of equations is:

\[ \boxed{x = -1,\; y = 2} \]

Hence, the two lines intersect at the point (−1, 2).