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
The slope-intercept form of a linear equation
What is y=mx+b ?
100
The number of solutions a linear system of equations may have.
What is 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?
Same Number, Same Variable, one positive and one negative.
100
What are the 3 steps in solving a system when it is given in the form of a word problem?
Create/make, 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
The number of solutions for parallel lines?
Zero
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate the variable
200
True or False
You only have to multiply one term by a number to use elimination in an equation in the system.
FALSE
200
The first thing I should do with a word problem when I try to create my system is to what?
Underline key parts of information/ figure out my 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
The number solutions of this graph
What is 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
The solution to this system of linear equations
What is (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
After using elimination to solve, the value for y.
16x − 12y = −40
−16x + 7y = 30
What is 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
The way to express the solution of a system of linear equations.
What is (x,y)?
500
The solution of this system of linear equations.
What is infinitely many solutions?
500
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
500
The solution for this system after using the Elimination method
−8x − 10y = 24
6x + 5y = 2
What is (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