Chapter three (Alg 2)

Question 1

System of two linear equations

Answer 1

two equations with two variables x and y

Question 2

of solutions of a linear system

Answer 2

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

Question 3

Substitution method

Answer 3

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

Question 4

Linear combination method

Answer 4

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

Question 5

Three dimensional coordinate system

Answer 5

Where Solutions of equations in three variables can be pictured.

Question 6

Z-axis

Answer 6

the vertical line through the origin representing height

The x and y axis start in a horizontal position

Question 7

Ordered Triple

Answer 7

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

Question 8

Octants

Answer 8

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)

Question 9

Linear equation in three variables

Answer 9

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

Question 10

Linear combination method (3-variable systems)

Answer 10

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