THE COMPOUND // FIELD NOTES // WEEK 04
Lines and systems begin
Field Book
Lessons 12 to 15
Due
Test 2 due ยท Supplement 4
Method
Paper first, every step
Escape 1 posts this week. The line work here is the toolkit the first case runs on.
What you have to be able to do
- Write equations of horizontal, vertical, and slanted lines
- Solve a system by substitution
- Solve a system by elimination
The procedures
Special linesField Book Lesson 12
- A horizontal line is y = a number. A vertical line is x = a number.
- Slope zero is horizontal. Undefined slope is vertical.
SubstitutionField Book Lesson 13
- Solve one equation for one variable.
- Substitute that expression into the other equation and solve, then back-substitute.
Writing the equation of a lineField Book Lesson 14
- Every case needs the slope m and the intercept b for y = mx + b.
- Three setups: given both, given slope and a point, given two points. Find m first, then b.
EliminationField Book Lesson 15
- Match the coefficient on x or y, but not both, across the equations.
- Add or subtract the equations to eliminate that variable, solve, back-substitute.
Worked: elimination
- Solve x + y = 10 and x - y = 4.
- Add the equations: 2x = 14, so x = 7.
- Back-substitute: 7 + y = 10, so y = 3.
Terms on the record
| Term | Meaning |
|---|
| system of equations | two or more equations analyzed together |
| substitution | replacing a variable with an expression equal to it |
| elimination | adding equations to remove one variable |