MISC.
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution1
Solving Systems of Linear Equations: Substitution2
How Many Solutions?
100
Is the given point a solution to the system of equations? Show work
Point: (2,6)
x + y = 8
3x - y = 0
Yes
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
Is the given point a solution to the system of equations? Show work
Point: (1/2, -2)
6x + 5y = -7
2x - 4y = -8
No
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 is a coefficient?
The number in front of a variable
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
What graph does a system of linear equations with no solutions look like? (use words, not images)
Parallel lines
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 many solutions does the system have?
3y + 4x = 6
12y + 16x = 24
These are the same exact line, therefore they have
Infinite Solutions
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 substitution method to solve the system of linear equations:
6x + 2y = 10
y = -3x -4
No solution
500
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
Zero or None