Objective 4

Linear Equations and Inequalities vocab linear equations: an algebraic equation in which each term is either a constant or a product of a constant and a single variable constant product For Example:

x+6= -3

constant single variable single variable product Inequalities: an algebraic sentence written

using the symbol ≥ , > , < , or ≤ ≤ < > ≥ ≥ sentence x-2 > 5 sentence symbol system of linear equations: two or more linear equations that use two or more variables. 2x-y= 10 two variables two more Elimination Method: also called the addition method because you need to eliminate one of the variables by adding. adding EXAMPLE substitution method:

solve one equation for one of the two variables, then substitute into the second equation one one substitute a+b = 30

-b = -b a = 30-b First start with two equations: a+b = 30 2a-3b = 10 Second you must subtract b from both sides now substitute (30-b) for a 2 - 3b = 10

2 -3b = 10

60-2b-3b = 10

60-5b = 10

60 = 10+5b

50 = 5b

10 = b elimination method: eliminate one of the variables by adding,

before adding you may need to multiply one

of the equations so that one of the variables has opposite coefficients. adding opposite

2x - 5y = 1

3x + 5y = 14

2x - 5y = 1

+ +

3x + 5y = 14

(2x - 5y) + (3x + 5y)= 1+14 5x = 15 x = 3 independent variable: the value being manipulated or changed Dependent variable:

observed result of the independent variable being manipulated a (30-b) + + Solving Problems With Linear Equations or Inequalities. XD Simplify by removing parenthesis and combining like terms. Isolate the variable on one side of the equation. Use multiplication or division to produce a coeffiecient of one for the variable. *When solving an inequality, you MUST reverse the symbol if you multiply or divide both sides! Use the solution to solve the question asked and check your answer :D.

2(X)-14= 9X

2X-14=9X. removing -14=9X-2X

-14=7X. Isolate subtracted 2x from one side -14/7=x

-2=x multiplication division divided by 7 MUST reverse multiply divide -2x > 10

-2x/-2 < 10/-2. < > 2X-14=9X Solution: x< -5 Tips and Examples: if there is a line under

the symbol the line

in the graph is SOLID.

If the sign is greater then shading will be above, vise versa. Representing Problems Using System of Linear Equations! *.*

Identify the quantities involved and the relationships between them. Represent the quantities invloved with two different variables or with expressions involving two variables.

2x+y=10 Write two independent equations that can be used to solve the problem.

2x+y=10 and x-3y=9 Solve a System of Linear Equations! O.O You can solve a system of linear equations algebraically and graphically. Two algebraic methods are substituion and elimination. Use graphs to show how many solutions a system of equations has: Write the equation in slope-intercept form to determine the number of solutions. TIP!!!!

Enter x and y coordinates in "Y=", then go to table to see a list of your x and y coordinates or go to graph to see a picture of your linear equation graphed. Using the substituion method: Elimination method problem: A common mistake is thinking that any given coordinate points on the line are the answer. THEY ARE NOT THEY

ARE NOT!!!!

x + y = -4

x - y = 2

x = 2 + y

2 + y + y = -4

2 + 2y = -4

2y = -6

y = 3

x = 5

x+y=8

x-y=-2

combine like terms 2x=6

x=3 add the x's and eliminate the y's combine both products Hope you do well on the TAKS :) x+10=-8 solution: x=-18 created by: Haley Lofton

Dana Joseph

Kristen Mayden

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# Objective 4- Linear equations and inequalities

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