GEOMETRY UNIT 1 WORKBOOK

GEOMETRY UNIT 1

WORKBOOK

FALL 2015 0

Algebra Review

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Geometry Algebra Review: 0-5 Linear Equations

If the same number is added to or subtracted from each side of an equation the resulting equation is true.

Example 1:

a. x + 8 =-5

b. n -15 = 3

c. p + 27 = 12

If each side of an equation is multiplied or divided by the same number, the resulting equation is true.

Example 2:

a. 5g = 35

b. - c =8 6

c. 4x = -3 7

To solve equations with more than one operation, often called multi-step equations, undo operations by working backward.

Example 3:

a. 9 p + 8 =35

b. 8x + 2= 14x - 7

When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols.

Example 4:

a. 4( x - 7) = 8x + 6

b. 1 (18 +12x) = 6(2x - 7)

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Geometry Algebra Review: 0-7 Ordered Pairs Points in the coordinate plane are named by ordered pairs of the form (x, y). The first number, or x-coordinate, corresponds to a number on the x-axis. The second number, or y-coordinate, corresponds to a number on the y-axis. Example 1: Write the ordered pair for each point. a. Point C b. Point D

The x-axis and y-axis separate the coordinate plane into four regions, called quadrants. The point at which the axis intersect is called the origin. The axes and points on the axes are not located in any of the quadrants.

Example 2: Graph and label each point on a coordinate plane. Name the quadrant in which each point is located. a. P(4, 2) b. M(-2, 4) c. N(-1, 0) Example 3: Graph a polygon with vertices P-1, 1, Q(3, 1), R(1, 4), and S(-3, 4).

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Remember lines have infinitely many points on them. So when you are asked to find points on a line, there are many answers. *Make a table. Choose values for x. Evaluate each value of x to determine the y. Plot the ordered pairs. Example 4: Graph four points that satisfy the equation = - - 2

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Geometry Algebra Review: 0-8 Systems of Linear Equations

Two or more equations that have common variables are called system of equations. The solution of a system of equations in two variables is an ordered pair of numbers that satisfies both equations. A system of two linear equations can have zero, one, or an infinite number of solutions. There are three methods by which systems of equations can be solved: graphing, elimination, and substitution.

Example 1: Solve each system of equations by graphing. Then determine whether each system has no solution, one solution, or infinitely many solutions.

a. = -3 + 1 = - 3

b. = 2 + 3 -4x + 2 = 6

It is difficult to determine the solution of a system when the two graphs intersect at noninteger values. There are algebraic methods by which an exact solution can be found. One such method is substitution.

Example 2: Use substitution to solve the system of equations.

a. = 3 -2 + 9 = 5

b. 3 + 2 = 10 2 + 3 = 10

Sometimes adding or subtracting two equations together will eliminate one variable. Using this step to solve a system of equations is called elimination.

Example 3: Use elimination to solve the system of equations.

a. -3 + 4 = 12 3 - 6 = 18

b. 3x + 7 =15 5 + 2 = -4

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