All about Systems of Equations
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution1
Solving Systems of Linear Equations: Substitution2
How Many Solutions?
100
What is a the linear equation we use? (slope-intercept form)
y=mx+b
100
14) What is the solution to the system of linear equations?
(2,2)
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
Solve the systems of equations using substitution:
y=3x-10
x=2
(2,-4)
100
How many solutions does the system of linear equations have?
One! (-4,-6)
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
What is the solution?
(-1,1)
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate the variable
200
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)
200
How many solutions does the system of linear equations have?
y = 3x - 5
y = 3x + 7
Zero or None
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point of intersection
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
What is your new (one) equation after performing substitution?
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
300
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
How many solutions does the system of linear equations have?
y = (-5/3)x + 3
y = (1/3)x - 3
One
400
At least how many linear equations will be in a system of linear equations?
At least 2 linear equations
400
Solve the systems of linear equations by graphing:
400
How would you isolate x in this equation?
6y+x=20
subtract 6y from both sides to get:
x=20-6y
400
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
400
How many solutions does the system of linear equations have?
y = 3x + 9
2y = 6x + 18
Infinitely many solutions
500
How do we write solutions to systems of linear equations?
(x,y)
500
Solve this by graphing:
2x - y = 4
x + 3y = 3
(3,2)
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
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
Zero or None