Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ 2x + y – 3 = 0 \]

\[ 2x – 3y – 7 = 0 \]

Solution

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

Equation (1):

\[ 2x + y – 3 = 0 \Rightarrow y = 3 – 2x \]

Equation (2):

\[ 2x – 3y – 7 = 0 \Rightarrow -3y = -2x + 7 \Rightarrow y = \frac{2x – 7}{3} \]

Step 2: Prepare Table of Values

For Equation (1): \(2x + y – 3 = 0\)

x	y
0	3
1	1

For Equation (2): \(2x – 3y – 7 = 0\)

x	y
2	-1
5	1

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

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

Join each pair of points to obtain two straight lines.

The two lines intersect at the point:

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

Conclusion

The graphical solution of the given system of equations is:

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

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