Week 22: Systems on the graph, and the main-equation substitution
Field Book
79 to 81
Due
Test 19 due
Method
Paper first, every step
You now have three ways to solve a system: graphing, substitution, and elimination. This week adds the graphical one and, more usefully, shows you what it looks like when there is no answer at all. Two lines that never meet have no solution. Two lines that are secretly the same line have infinitely many. Both of those are real answers, not mistakes.
What you have to be able to do
Solve a four-unknown problem by substituting every given relationship into one main equation
Solve a system by graphing
Recognize an inconsistent system and a dependent one
The procedures
The main equation
Pick the one equation that carries the quantity the question actually asks for. That is the main equation.
Take every other relationship you were given and write each one so it states a single unknown by itself.
Substitute those into the main equation, one at a time, until only one unknown is left, then solve.
Solving a system by graphing
Put both equations in y-equals form and graph them on the same grid.
The point where they cross is the solution, and it satisfies both equations at once.
If the lines are parallel, there is no solution. If they lie on top of each other, every point is a solution.
two equations that are the same line, infinitely many solutions
solution of a system
the point that makes both equations true at once
Check yourself
1. (2 × 103)(4 × 102)
2. (9 × 108) ÷ (3 × 102)
3. Two lines have the same slope but different intercepts. How many solutions?
reveal answers
8 × 105 · 3 × 106 · none, they are parallel
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 22, systems on the graph, and the main-equation substitutionalgebra 1 · oda