# Using graphs to solve equations

**Using graphs to solve equations**

To solve equations using graphs, the equation should be split into two and plotted on a graph. The points where the two functions cross is where the solutions will be found. For example:

2*x²* – 5 = 3*x *(split the equation as two separate functions:

*y* = 2*x²* – 5

*y* = 3*x*

These are plotted on a graph as follows:

The points where these two functions intersect will provide the following solutions for the equation:

The intersections are (-1, -3) and (2.5, 7.5) which when replaced in the 2*x²* – 5 = 3*x *equation will provide the following solutions:

*x* = -1

*x* = 2.5