All about Systems of Equations
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution
Solving Systems of Linear Equations: Elimination
Applications of Systems
100
What is a the linear equation we use? (slope-intercept form)
y=mx+b
100
What are the types of solutions that a system of linear equations can have?
one, none/zero, or infinitely many solutions
100
If we were to do substitution and have a graph of the same system of equations would we get the same solution?
Yes.
Every equation graphs a specific line so no matter how you solve, you get the same solution!
(Graphs are definitely easier, but we don't always have graphed systems!)
100
What must you have to use the Elimination Method?
Line up variables, Same coefficient, change signs, ADD!!
100
What are the 3 steps in solving a system when it is given in the form of a word problem?
creat the system, solve, and analyze.
200
True or False:
It does not matter which method you use when solving systems of linear equations because they will all give you the same answer.
True
200
How many solutions will a set of parallel lines have?
Zero
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate the variable
200
Find the error.
2x+3y = 6 -------> -2x+3y= -6
4x+ 6y = 12 ------> 2x+3y = 6
Need to change the sign on the top +3y to -3y
200
The first thing I should do with a word problem when I try to create my system is to what?
create bullet points and identify variables
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point of intersection
300
How many solutions are represented in the graph?
1 solution
300
What is your new (one) equation after performing substitution?
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
300
What do I Multiply by the top equation to use Elimination?
x + 7y = 0
2x − 8y = 22
-2
300
Create an equation from the following information:
I have 8 siblings in my family. How many brothers and sisters do I have?
s + b = 8
400
At least how many linear equations will be in a system of linear equations?
At least 2 linear equations
400
14) What is the solution to the system of linear equations?
(2,2)
400
How would you isolate x in this equation?
6y+x=20
subtract 6x from both sides to get:
x=20-6x
400
Perform Elimination on the System below. What is the value of y?
16x − 12y = −40
−16x + 7y = 30
y=2
400
Create and Solve the System.
Heather has been offered two options for her salary as a trainer at the gym. Option A would pay her $25,000 plus $15 for each training session. Option B would pay her $10,000 + $40 for each training session. How many training sessions would make the salary options equal? Let s be salary earned and n be the number of training sessions.
s=25000 + 15n
s=10000 + 40n
600 = n
500
How do we write solutions to systems of linear equations?
(x,y)
500
What is the solution to the system of linear equations?
Infinitely many solutions
500
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
500
Use the Elimination method to solve the system of linear equations:
−8x − 10y = 24
6x + 5y = 2
(7,-8)
500
Create and Solve the System.
When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for 20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes on the elliptical trainer and 30 minutes circuit training she burned 473 calories. How many calories does she burn for each minute on the elliptical trainer? How many calories for each minute of circuit training?
10e + 20c = 278
20e + 30c = 473
e= 11.2
c = 8.3