Methods
Graphing
Substitution
Elimination
Miscellaneous
100
What are the three practiced methods used for solving systems of equations?
Graphing Method, Substitution Method, and Elimination Method.
100
When graphing a system of equations, the solution is where ____________________
The two line intersect (aka where they touch).
100
To use the substitution method, what is the first step that needs to happen?
Solve one of the equations for a single variable (either variable will work)
100
What is the first step we need to do when using the elimination method?
Make sure at least one variable will cancel out when adding the equations (Multiply if necessary).
100
On Wednesdays, _____________
WE WEAR PINK!!
200
Which method would be the fastest when solving this system of linear equations?
4x-3y=-2
2x-3y=6
The Elimination Method
200
What does a system of linear equations, with no solution, look like?
Two Parallel Lines
200
Once one of the equations is solved for a single variable, what do you do with that solved equation?
Plug it in to the unsolved equation for the variable we solved for.
200
What is the goal when using the Elimination Method?
To "eliminate" at least one of the variables when adding the equations together.
200
Two lines have the same slopes and different y-intercepts. How many solutions would this system of equations have?
No Solution, the lines would be parallel.
300
Which method would be fastest to solve this system of linear equations?
y=-2x+3
y=4
The Substitution Method
300
What does a system of linear equations, with one solution, look like?
Two different lines with one intersection (aka two lines touching once)
300
The solution of the following system of equations:
y=-3
y=6x+3
(-1,-3)
Show your work.
300
The solution of the following system of equations:
3x-6y=3
4x+6y=32
(5, 2)
Show your work.
300
Two lines have the same slopes and y-intercepts. How many solutions would this system of equations have?
Infinitely Many Solutions, it's the same line twice.
400
In what method do you replace a variable with something of equal value?
The Substitution Method
400
What does a system of linear equations, with infinitely many solutions, look like when graphed?
The same line twice (one on top of the other)
400
The solution of the following system of equations:
y=-3x
-3x+3y=0
(0, 0)
Show your work.
400
The solution of the following system of equations:
x+2y=13
x-y=-5
(1, 6)
Show your work.
400
Your final solution to a system of equations will always be written as ______
A point (x,y)
500
What method are you using when you attempt to have one variable with the same number but opposite signs in a system?
The Elimination Method
500
What is the solution to this system of equations?
(1, 2)
500
The solution of the following system of equations:
y=x-2
y=-2/3x+3
(3, 1)
Show your work.
500
The solution of the following system of equations:
2x+8y=-22
x+5y=-12
(-7, -1)
Show your work.
500
How would you check if (2, 5) is a solution to a system of equations?
Plug in 2 for x and 5 for y in both equations. If it works for both equations, it's a solution. Otherwise, it is not a solution.