6.1 Functions and Equations of Two Variables
Systems of Equations of two variables
Consider the following system of equations:
y=x+2
y = -x + 4
Our job: find a point (pair of numbers (x,y)) that satisfies both
equations.
Note: the graph of an equation is the set of all points (x, y) that
satisfy the equation
If we graph these equations, we get:
4
y
y=x+2
y = -x + 4
x
4
 describe the point that satisfies both equations
 what are its coordinates?
 does that point, in fact, satisfy both equations?
graphical method (just shown):
 can be an effective way, using a graphing calculator
 we will mainly cover systematic, symbolic methods
 e.g. substitution and elimination
Substitution: board demo (also, see book)
6.1-1
Reminder - word problem format again
Some of the HW problems will be marked “word problem
format”. Use word problem presentation rules:
1. Start with two let’s. Since these are two-variable
problems, you will need to say something like:
let x = speed of first car let y = speed of second car
2. Write a system of two equations with two variables,
solve, and check
3. Answer the question asked (in the language of the
problem - no mention of “x” or “y”). Attach units,
where applicable.
Note: “word problem format” problems not presented as
above are too hard to grade, and can receive no credit.
Functions of two variables
f(x, y) = x + 2y
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what does this mean?
f is a function
but instead of one input (x), it has two inputs (x and y)
it’s called a function of two variables
f(1, 2) = 5
f(0, 3) = ??
f(r, h) = r2h : a function of two variables that computes
the volume of a cylinder of radius r and height h
6.1-2