# Solving linear equations - two views

- Author:
- Judah L Schwartz

- Topic:
- Equations, Linear Equations

**Here are two views of symbolically representing two linear functions plotted in the {x,y} plane.**

**1) A pair of simultaneous linear equations of the form ax + by = c and Ax + By = C**, or 2)

**A single equation of the form px + q = Px + Q.**

**If you regard the two linear functions as a**

__of simultaneous linear__*pair*__then the solution set is the point in the {x,y} plane where the graphs of ax + by = c and Ax + By = C intersect.__*equations**[what is the significance of the value(s) of y in the solution point {x,y}? How many such values are there? Why?]***If you regard the two linear functions as a**

__of the form px + q = Px + Q then the solution set is the point on the x axis whose x coordinate is the x coordinate of the intersection point of the two graphs.__*single equation***Which formulation do you prefer ? Why ?**

*Does this perspective extend to functions other than linear - i.e., F(x) = G(x) as opposed to y = F(x) and y = G(x) ? Does this perspective extend to functions of more than one variable - i.e., F(x,y) = G(x,y) as opposed to z = F(x,y) and z = G(x,y) ?*

**What problems could/would you pose to your students based on this applet ?**.