Linear Equation Notes
October 22, 2015
Notes: Distributive Property, Combining like
terms, and solving equations.
Linear Equation Notes
Combining Like Terms
~Terms must have same variable and exponents~
Ex. 1) 3x+2y-x+2
2
Ex.2) 3x -2x+5x
October 22, 2015
Linear Equation Notes
Distributive Property
Ex 1.) 3(2x+6)
Ex. 2) 4x(3x+2)
October 22, 2015
Linear Equation Notes
October 22, 2015
Notes on Solving Equations:
~Start by Combining any like terms and distributing.
2(x+3)= 4x-3+x
~Get rid of any fractions by multiplying every term by the denominator.
3x-5 -2=6
2
~Move all the #'s to one side (everything you are not solving for) and the
variable you are solving for on the other side.
2x+6=5x-3
~Divide each side by the coefficient in front of the variable you are
solving for.
9=3x
Linear Equation Notes
October 22, 2015
Solving Inequality Equations
~Everything is the same as regular equations, except when you
divide or multiply by a negative the sign switches direction.
~Once we solve, we can graph on a number line.
Linear Equation Notes
October 22, 2015
Graphing Inequalities on a Number Line:
Name
Symbol
Type of Dot
Greater Than
Open
Less Than
Open
Greater Than or equal to
Closed
Less than or equal to
Closed
~read the number sentence to figure out what way your arrow
will go.
Ex. 1) 3 > x
-5
-4
-3
-2
-1
0
1
2
3
4
5
Step 1: Put the correct dot on your number (open or closed)
Step 2: Plug in a number for x. (smaller or bigger then your
number, see if it makes sense.)
3 > 1 or 3 > 5
Whatever one is true, shade in that direction.
Linear Equation Notes
-10
-9
-8
-7
-6
October 22, 2015
-5 -4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
Graphing inequalities on a graph
Symbol
Type of Line
Shading (y comes first)
Dotted
Up
Dotted
Down
Solid
Up
Solid
Down
Linear Equation Notes
October 22, 2015
Ex. 1
y x+2
Linear Equation Notes
October 22, 2015
Ex. 2
y 4
Linear Equation Notes
October 22, 2015
Ex. 3
x -2
Linear Equation Notes
Try on your own:
y+1 3x-3
October 22, 2015
Linear Equation Notes
October 22, 2015
System of Equations
You will have 2 equations and you have to find a solution that
works in both.
~We will work with equations and inequalities.
Linear Equation Notes
October 22, 2015
Ex. 1
x -2
y 4
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
Linear Equation Notes
October 22, 2015
To solve a system of equation in the calculator
Linear Equation Notes
October 22, 2015
Warm Up
Ex. 1
A number is multiplied by 2, and then the product is added to 9.
The result is 49. What is the number?
Linear Equation Notes
October 22, 2015
Ex. 2
Find three consecutive
integers whose sum is 36?
Linear Equation Notes
October 22, 2015
Ex. 3
After Ricardo received his allowance for
the week, he went to the mall with some
friends. He spends half of his allowance on
a new paperback book. Then he bought
himself a snack for $1.25. When he
arrived home, he had $5.00 left. How much
was his allowance?
Linear Equation Notes
October 22, 2015
Ex. 4
At a sale on winter clothing, Cody bought
two pairs of gloves and four hats for $43.
Tori bought two pairs of gloves and two
hats for $30. What were the prices for
the gloves and hats.
Linear Equation Notes
October 22, 2015
Ex. 5
Trisha and Byron are washing and
vacuuming cars to raise money for a class
trip. Trisha raised $38 washing 5 cars and
vacuuming 4 cars. Byron raised $28 by
washing 4 cars and vacuuming 2 cars. Find
the amount they charged to wash a car
and vacuum a car.
38=5x+4y
28=4x+2y
solve for y.
38=5x+4y
-5x -5x
38-5x=4y
4
4
(38-5x)÷4=y
28=4x+2y
-4x -4x
28-4x=2y
2
2
(28-4x)÷2=y
After you have solved for y, you plug both
equations into y= in the calculator.
Press graph. If your intersection does not
show up try "zoom fit" or changing your
window.
Once you see the intersection on the screen,
press "2nd" "Trace" "Intersect, enter" "enter"
"enter" "enter"
You should get x=6 and y=2.
Final Answer:
Washing cars is $6 and Vacuuming cars is $2