Algebra 2 - Chapter 4 (Systems of Equations and Inequalities)

Command you use in the MATH section of "Matrix" to solve a matrix

rref

What you enter into your matrix if one of your equations is missing a variable

0

Example of how to know your system is dependent

12=12 (2 of the same numbers equal each other and your variables are gone)

Example of how to know your system is inconsistent

12=13 (2 different numbers equal each other and your variables are gone)

Dependent System

2 lines on a graph that are the exact same line and lie on top of each other and thus have infinite solutions

Independent System

2 lines on a graph that intersect at one point and thus have one solution (x,y)

Inconsistent System

2 lines on a graph that never intersect, have no solution, and are parallel to each other

A 2 x 3 matrix has ____ rows and ____ columns

2 rows, 3 columns

How to write solution for a dependent system

An ordered pair (x, expression for y that you found by isolating y)

How to write the solution of a system of equations that includes 2 variables, x and y

An ordered pair (x,y)

(Time)(Rate)=

Distance

How to solve using substitution

Isolate x or y in one of the equations. Take the expression you just got and substitute it into the OTHER equation so you have an equation with one variable. Solve for that variable, then substitute that value into either original equation to find the 2nd variable.

How to solve by graphing

Isolate y in each equation and plot using the slope and y-intercept. Your solution is the point where they intersect.

When graphing a solution set of a system of inequalities, the only region that should be shaded is the _____.

Overlapping region between the solutions of each separate inequality.

Section of "Matrix" that you go into to enter a matrix

"EDIT"

How to solve using the addition method

The coefficients of one of your variables need to be opposites (same number, but one is + and the other is -). If you don't have this, multiply one or both equations by something to get opposite coefficients. Add equations so one variable cancels. Solve for remaining variable and use that to find the other variable.

What you need to show on your test if you're solving by a matrix

The matrix you plug into your calculator

Easiest variables to isolate when solving by substitution

Those that have 1 as a coefficient

The rate of a boat going with a current is _____.

x + y

The rate of a boat going against the current is _____.

x - y

The rate of a boat in calm water is _____. The rate of the current is _____.

x, y