Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ x + y = 3 \]

\[ 2x + 5y = 12 \]

Solution

Step 1: Write Both Equations

Equation (1):

\[ x + y = 3 \Rightarrow y = 3 – x \]

Equation (2):

\[ 2x + 5y = 12 \Rightarrow 5y = 12 – 2x \Rightarrow y = \frac{12 – 2x}{5} \]

Step 2: Prepare Table of Values

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

x	y
0	3
3	0

For Equation (2): \(2x + 5y = 12\)

x	y
1	2
6	0

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

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

Join each pair of points to obtain two straight lines.

The two lines intersect at the point:

\[ (1,\,2) \]

Conclusion

The solution of the given system of equations is:

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

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