Download LESSON 1.3: LINE OF BEST FIT --Best for systems when there is a

PORTFOLIO PAGE -- LINEAR FUNCTIONS 2
HONORS ALGEBRA 2
GENERAL FORMS OF EQUATIONS:
Slope-Intercept Form: y = mx + b; m is slope, b is y-intercept
Point-Slope Form: y – y1 = m(x – x1)
Standard Form: Ax + By = C
LESSON 1.3: LINE
To find the LINE
a)
b)
c)
d)
e)
OF
BEST FIT
OF BEST FIT:
Determine independent (x) vs. dependent (y) variable
Plot data points
Estimate trend line
Choose two points ON THE LINE
Calculate slope and write equation of line.
(start with Point-slope form)
SYSTEMS
OF
x
Y
2
3
4
4
7
6
9
8
EQUATIONS
A system of two linear equations in two variables, x and y, consists of two equations of the form
𝒂𝒙 + 𝒃𝒚 = 𝒄
൜
.
𝒅𝒙 + 𝒆𝒚 = 𝒇
A solution to the system is an ordered pair (x, y) that satisfies BOTH equations.
Ex: Solve the system by graphing:
ቊ
2𝑥 + 4𝑦 = 12
𝑥+𝑦 = 2
SOLVING SYSTEMS USING SUBSTITUTION
--Best for systems when there is a variable term that has a coefficient of 1
𝑥 + 6𝑦 = 2
ቊ
5𝑥 + 4𝑦 = 36
SUBSTITUTION METHOD:
1) Solve one equation for one of its
variables. (Hint: look for a coefficient
of 1)
2) Substitute this expression into the
other equation. Now you have an
equation with only one variable. Solve it.
3) Substitute this value in the revised
first equation and solve.
4) Write an ordered pair. Check the
solution in each equation.
SOLVING SYSTEMS USING ELIMINATION
--get opposite coefficients on same variable terms, then add equations
ELIMINATION METHOD:
1) Arrange equations with like terms in
columns (like terms under each other).
2) Multiply one (or both) equation(s) by a
number to obtain opposite coefficients for
either the x or the y terms. (LCM of the
coefficients)
3) Add the equations (one variable should
now be eliminated). Solve the resulting
equation.
4) Substitute the result of step 3 into one
of the original equations to solve for the
other variable.
5) Write in ordered pair form and check the
solution in each of the original equations.
ቊ
Algebraic solutions indicating
a) no solution
2𝑥 + 8𝑦 = −8
3𝑥 − 5𝑦 = 22
b) infinitely many solutions
6𝑥 − 3𝑦 = 2
2
ቐ
−6𝑥 + 3𝑦 =
3
𝑥 + 5𝑦 = 1
ቊ
2𝑥 = 2 − 10𝑦
LESSON 1.4: SOLVING SYSTEMS
Triangular Form:
THREE VARIABLES
Elimination:
x  y  z  4

y  z  5
z  3

APPLICATIONS
IN
 2 x  y  3 z  7

x  2 y  z  4
2 x  3 y  2 z  10

OF
SYSTEMS
OF
EQUATIONS (2-
AND
3-
VARIABLE SYSTEMS)
Ex1: There are 55 coins made up of
dimes and nickels in a piggy bank.
The total value is $4.00. Write the
system to find how many coins
there are of each type.
Ex2: The difference of two
numbers is 24. Their sum is 60.
Write the system to find the two
numbers.
Ex3: A stadium has 49,000 seats.
Seats sell for $25 in Section A,
$20 in section B, and $15 in Section
C. The number of seats in Section
A equals the total number of seats
in Sections B and C. Suppose the
stadium takes in $1,052,000 from
each sold-out event. How many
seats does each section hold?
Ex4: A change machine contains
nickels, dimes, and quarters. There
are 75 coins in the machine, and the
value of the coins is $7.25. There
are five times as many nickels as
dimes. Find the number of coins of
each type in the machine.
M. Murray