Unit 2 Solving Systems on equations by graphing
intersecting lines
one solution
unbounded region
open and can go on forever
substitution method
solve one equation for one variable then substitute the expression into other equation and solve, then substitute variable into other equation and solve
systems of equations
2 or more equations with the same variables (solution is an ordered pair)
linear programming
Method to find max and min values -- define variables. Write The inequalities. Graph the inequalities. Find the vertices. Develop a linear function. Find a maximum or minimum. Answer the problem in a sentence.
ordered triple
a solution to the system in which you solve for 3 variables (x, y, z)
bounded region
enclosed shape
graphing method
graphing the lines and finding where they intersect
constraints
inequalities (lines themselves)
same line
infinitely many solutions
Systems of linear inequalities
means finding the ordered pairs that satisfy all of the inequalities in that system. steps: Graph each inequality, shade appropriate region. Identify the region that is shaded for all of the inequalities. This is the solution to the system.
elimination method
multiply one or both equations by a number to result in 2 equations that have opposite terms. Add equations, eliminations one variable, solve. Substitute to solve for the variable
parallel lines
no solution
feasible region
the shaded area after the inequalities are graphed