Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ x – y + 1 = 0 \]

\[ 3x + 2y – 12 = 0 \]

Solution

Step 1: Write Both Equations in a Convenient Form

Equation (1):

\[ x – y + 1 = 0 \Rightarrow y = x + 1 \]

Equation (2):

\[ 3x + 2y – 12 = 0 \Rightarrow 2y = 12 – 3x \Rightarrow y = 6 – \frac{3}{2}x \]

Step 2: Prepare Table of Values

For Equation (1): \(x – y + 1 = 0\)

x	y
0	1
2	3

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

x	y
0	6
4	0

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

• Line 1: (0, 1) and (2, 3)
• Line 2: (0, 6) and (4, 0)

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 given pair of linear equations intersect at the point (2, 3).