All about Systems of Equations
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution
Special Cases
100
What is a the linear equation we use? (slope-intercept form)
y=mx+b
100
How many solutions can a system of linear equations 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
True or False: A system that has infinite solutions would be:
2x+y=9
-2x+y=9
False:
The slopes of the lines are 2 and -2, meaning it would have one solution.
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
How many solutions does the following system have?
y=2x+4
y=2x+5
No solution
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point (x and y value of) where the 2 lines intersect.
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
How many solutions does this system of equations have?
y+3x=7
y+3x=7
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
How many solutions does the following system of equations have?
y-9=3x
y=9x+3
One solution, different slopes
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
How many solutions does the following system of equations have?
y-2x=4
y-4=2x
Infinitely many solutions.
Write the equations in y=mx+b
y=2x+4
y=2x+4
(isolate the y)