How to Graph Simultaneous Equations

An equation yields a set of x and y coordinates that, when plotted on a Cartesian Coordinate Plane, produces a particular graph. When two or more linear equations are plotted on the same plane, they are known as simultaneous equations. It is often necessary in mathematics to find the intersection point(s) of simultaneous equations. While this can be done algebraically, graphing the equations (functions) and physically determining the point of intersection is fundamental to further mathematical inquiry.

Things You'll Need

• Equations Graph Paper

Instructions

1. Draw a Cartesian Coordinate Plane (an x and y axis) on your graph paper.

2. Write the simultaneous equations on another piece of paper. Rearrange (if necessary) the equations algebraically to solve for y. The equation should be in y=mx+b format. Note the m value and the b value.

3. With your pen or pencil, plot the y intercepts of the two equations. The y intercepts are the b values you discovered when rearranging the equations. The y intercepts will lie on the vertical y axis.

4. Plot the remaining points for each equation. The remaining points can be determined with the m value, or the slope, for each function. The slope is in rise/run format. For example, if one of the equations was y=(3/4)x+4, I would place my y intercept point at (0,4), rise 3 units and run 4 units to the right to find the next point (3,8). Continue to plot points until the edges of the graph paper are reached.

5. Connect the points for each equation. You have just graphed simultaneous equations. If you wish to find the point of intersection, or solution, for the simultaneous equations, note the x and y coordinates where the lines cross.

Tips & Warnings

• Plot each line separately to avoid confusion. Write neatly, and always check your work.

References

• Graphing Simultaneous Equations Tutorial

Resources

• The Math Page: Simultaneous Equations