3-1: Graphing Systems of Equations
Objective:
• To solve a system of equations by graphing (by hand and with a calculator).
Vocabulary:
System of Linear Equations:
System Solution:
a set of two or more linear equations with the same variables
an ordered pair that satisfies all the equations in the system; it's where the lines intersect
EX #1:
3 things can happen when you graph two lines:
• they can intersect at one point (independent)
• they can be the same lines (dependent) or
• they can be parallel lines (inconsistent) Vocabulary:
Independent System: where the solution is a unique ordered pair (x, y); the lines intersect at one point Dependent System: where the system does not have a unique solution;
infinitely many ordered pairs work (same lines) Inconsistent System: where there is no solution (parallel lines) Checking Solutions:
Looks like the solution is (­3, ­2)?
Try it in both equations to check!!!
distance
time
5x + 40
9x
5x + 40
9x
The father caught up to his daughter after 10 seconds.
When the father caught up to his daughter, they were 90 meters from where they started.
independent
( ­ 3, 2 )
independent
( 5, 4 )
inconsistent
none
dependent (consistent)
infinite