# Solving Equations Graphically

Learn how to solve equations using points of intersection of graphs

###### Author and programmer: Ron Barrow

UK Years 10-12, KS4, KS5, Higher GCSE Mathematics, Grades C - A*, Core AS Level - Number, Algebra and Graphs

TweetInstructions below See also: Simultaneous Equations solved Graphically Circles and Lines

## How to Use this Applet

Look at the initial position of the two lines on the graph above. You can see that they cross in two places. What are the x-coordinates of the points where they cross, and how does that tie in with the solution of the equation at the bottom left of the screen? Look at that equation carefully. What is the significance of the left-hand side and right-hand side? That should give you a starting point for investigating this topic. If you go to the bottom left you can chose whether to look at one quadratic and one straight (linear) graph, or two quadratic graphs. You can move Graph 1 by varying A, B and C. You can vary Graph 2 by varying D, E and F (although clicking D will have no effect if you have chosen Graph 1 to be straight (linear)). Go ahead. Try it. Are there always solutions? sometimes only one? Investigate!