# Elementary Algebra (Lec01)

## yukita@k.hosei.ac.jp

### •Expand and Factor

Factorization over Z[I], where I=Sqrt[-1].

Algebra modulo p.

### •Collect

Collecting like terms.

### •Together, Apart, and Cancel

### •Coefficient

### •Solve and Reduce

System of equations

#### •Example 1

Let C be a hyperbola defined by x^2-y^2=1. Let L be a line defined by -2x+3y=5. Find the intersection of C and L.

#### •Example 2

Find a circle that passes through all the intersection points of C and L (in Example 1), and also passes through point (5,0).

### •Quotient and Remainder

### •Exercises

#### •Problem 1

Let C be a circle defined by x^2+y^2= 1. Let L be a line defined by 3x+4y=5. Find the intersection of C and L.

##### •Solution

We must solve the following system of equations.

We see that the straight line is tangent to the circle.

Note that the default point size is 0.008.

Converted by *Mathematica*
(May 8, 2003)