Graphical Solution of Equations

Introduction

Graphical solutions involve using graphs to find the solutions of equations. This method is particularly useful for solving linear and quadratic equations.

In this section, we will explore how to use graphs to solve:

• Linear equations
• Pairs of linear equations (simultaneous equations)
• Quadratic equations

Graphical Solution of Linear Equations

A linear equation in two variables, such as y = mx + c, can be represented graphically as a straight line. The solution of the equation is the point where the line crosses the x-axis (i.e., where y = 0).

Steps to Solve Graphically

1. Plot the graph of the equation on a coordinate plane.
2. Identify the point where the line crosses the x-axis.
3. The x-coordinate of this point is the solution to the equation.

Graphical Solution of Simultaneous Equations

To solve a pair of linear equations graphically, plot both lines on the same graph. The solution is the point where the two lines intersect.

Steps to Solve Graphically

1. Plot the graph of each equation on the same coordinate plane.
2. Find the point of intersection of the two lines.
3. The coordinates of this point are the solutions to the equations.

Graphical Solution of Quadratic Equations

A quadratic equation can be represented graphically as a parabola. The solutions of the equation are the x-coordinates of the points where the parabola crosses the x-axis.

Steps to Solve Graphically

1. Plot the graph of the quadratic equation on a coordinate plane.
2. Identify the points where the parabola crosses the x-axis.
3. The x-coordinates of these points are the solutions to the equation.