# Chapter three (Alg 2) Flashcards

1
Q

System of two linear equations

A

two equations with two variables x and y

2
Q

of solutions of a linear system

A

a pair of lines that intersect, lines have different slopes, only one solution
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Identical lines, same slope and y-intercept with infinitely many solutions
{}
Parallel lines, same slope with different y-intercepts, no solution

3
Q

Substitution method

A

Solving a linear system without graphing
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Substitute the expression into the other equation and solve for the other variable

4
Q

Linear combination method

A

obtained by multiplying one or both equations or adding the resulting equations

5
Q

Three dimensional coordinate system

A

Where Solutions of equations in three variables can be pictured.

6
Q

Z-axis

A

the vertical line through the origin representing height

The x and y axis start in a horizontal position

7
Q

Ordered Triple

A

Each point in space represented by (x, y, z)

8
Q

Octants

A

The planes are divided into 8 of these, the first octant is where all values of (x, y, z) are positive. (Just imagine 2 levels of 4 cubes representing the octants)

9
Q

Linear equation in three variables

A

Ax + by + cz = d, d is the z intercept

10
Q

Linear combination method (3-variable systems)

A

Rewrite the linear system in tree to two variables, Solve the new linear system for both of its variables, substitute the values found in step 2 into one of the original equations and solve for the remaining variable