Graphing
Draw a picture of a system of linear equations that has no solutions.
To use substitution, what does at least one the equation need to look like?
a variable has to be isolated
ex: x=# y=#
What format is best for elimination? Give an example of a linear equation in that form.
Standard form
ex: Ax+By=C or -4x+6y=13
What are the three methods for solving a system of equations?
Graphing, Substitution, & Elimination
What is the equation for slope-intercept form?
y=mx+b
Draw a picture of a system of linear equations that has infinite solutions.
COMING TO CHECK! But should be THE SAME LINE
The solution of the following system of equations:
y=-3
y=6x+3
(-1,-3)
Solve using elimination
-5x+4y=30
-3x-4y=-14
(-2,5)
What method would you use to solve the following systems, explain your reasoning?
8x-y=8
x+y=32
Substitution or Elimination
What is a system of equations?
more than one equation
Draw a system of linear equations that has a solution at (-4,2)
COMING AROUND TO CHECK
The solution of the following system of equations:
x=7
2x+5y=4
(7,-2)
Solve using elimination
3x-6y=3
4x+6y=32
(5,2)
What method would you use to solve the following systems, explain your reasoning?
y=1/2x-5
y=5/2x+2
Graphing
If two lines are parallel, how many solutions will it have?
no solutions, zero or none
Find the slope and y-intercept for the following equations:
equation 1: y=-7x-4
equation 2: 2x+y=8
equation 1: m=-7 b=-4
equation 2: m=-2 b=8
Use substitution to solve the following system:
y=3x-7
y=4x+8
(-15,-52)
The solution of the following system of equations using elimination:
2x+8y=-22
x+5y=-12
(-7,1)
How could you justify using the graphing method for this system of equations? Explain your reasoning.
Equation 1: 2x+y=-5
Equation 2: y=-2x-6
EX:
Equation 1 is already in slope-intercept form & equation 2 only takes 1 step of algebra to transform it from standard to slope-intercept form (subtracting 2x)
The format used to write a single solution to a system of linear equations.
an ordered pair or (x,y)
Transform from standard form to slope-intercept form.
6x-2y=-4
y=3x+2
Use substitution to solve the following system:
2x-y=-12
x+4y=3
(-5,2)
The solution of the following system of equations using elimination:
2x+4y=-12
3x+3y=6
(10,-8)
What method would you use to solve this system of equations? Explain your reasoning.
Equation 1: 12x+y=450
Equation 2: -24x-18y=320
substitution or elimination
Write a system of equations for the word problem: DO NOT SOLVE
A concert offers two types of tickets: a VIP ticket for $120 and a general admission ticket for $40. If they sold a total of 60 tickets, earning $5400 in revenue, how many of each ticket type were sold?
120x+40y=5400
x+y=60
or
120v+40g=5400
v+g=60