Graphical Solution of a Pair of Linear Equations

Video Explanation

Question

Solve the following system of equations graphically:

\[ x – 2y = 5 \]

\[ 2x + 3y = 10 \]

Solution

Step 1: Write Both Equations in a Convenient Form

Equation (1):

\[ x – 2y = 5 \Rightarrow x = 5 + 2y \]

Equation (2):

\[ 2x + 3y = 10 \Rightarrow 2x = 10 – 3y \Rightarrow x = \frac{10 – 3y}{2} \]

Step 2: Prepare Table of Values

For Equation (1): \(x – 2y = 5\)

x	y
5	0
1	-2

For Equation (2): \(2x + 3y = 10\)

x	y
5	0
2	2

Step 3: Graphical Representation

Plot the following points on the same Cartesian plane:

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

Join each pair of points to obtain two straight lines.

The two lines intersect at the point:

\[ (5,\,0) \]

Conclusion

The graphical solution of the given system of equations is:

\[ \boxed{x = 5,\; y = 0} \]

Hence, the given pair of linear equations intersect at the point (5, 0).