# Chapter three (Alg 2) Flashcards

System of two linear equations

two equations with two variables x and y

of solutions of a linear system

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

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Parallel lines, same slope with different y-intercepts, no solution

Substitution method

Solving a linear system without graphing

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Substitute the expression into the other equation and solve for the other variable

Linear combination method

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

Three dimensional coordinate system

Where Solutions of equations in three variables can be pictured.

Z-axis

the vertical line through the origin representing height

The x and y axis start in a horizontal position

Ordered Triple

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

Octants

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)

Linear equation in three variables

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

Linear combination method (3-variable systems)

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