Linear equations

Variable - Any quantity in an equation which we do not know is called a variable.

Constant - Anything in an equation which can take on only one value is called a constant.

Term - The product of a constant and a variable raised to some power is called a term.

Coefficient - The constant in such product is called a coefficient

x and y are variables

2 is a constant term

3 is the coefficient of x

Is  $x+\sqrt{x}=3$  a linear equation?

How about  $xy=4$  ?

One equation, add/abstract then divide/multiple

Two equations: Substitution or Elimination

By using elimination, we get 0 = 3

never be true. no solution.

Define all the variables

Write the equations described by the problem

Solve the equations

Step 1: variables - Johnny's age is x, Gina's age is y.

Step 2: x = 2y, x = y + 5

Step 3: Solve it.

"Moving" problem - rate x time = distance

"Job/Project" problem - (time at work)(fraction of work in one unit of time) = (fraction of job done)

In one hour, pipe A can fill 1/5 of the pool. pipe B can fill 1/4.

In one hour, both of them fill (1/5+1/4)

For x hours, they fill x(1/5+1/4). ( when this fraction is 1, the pool is full)

Variables - Tom x, Huck y, Jim z

Equation - 4(1/x+1/y)+2(1/x+1/y+1/z) = 1

4(1/x + 1/y) +5(1/x+1/y) =1