Algebra II Notes
Pg 41
Chapter 3 Section 1
Define the following:
System of Equations - _________________________________________________
_____________________________________________________________________
The solution to a system is in the form of _________________________________
Example: Solve the system of equations 2x + y = 5 and x – y = 1 by graphing!
Solve the system of equations:
9x – 6y = 24
6x – 4y = 16
Pg 42
Solve the system of equations:
3x + 4y = 12
2x + 8y = 16
Define the following:
Consistent & dependent - _______________________________________________
_____________________________________________________________________
Consistent & independent - _____________________________________________
_____________________________________________________________________
Inconsistent - _________________________________________________________
_____________________________________________________________________
Homework: A#
Algebra II Notes
Pg 43
Chapter 3 Section 2
Solve a system of equations using ________________________________.
When we do this please follow these steps until you are confident in your steps!
Step 1:
Step 2:
Step 3:
Let’s give it a try! Solve the system of equations 2x – y = 9 and x + 3y = -6.
Pg 44
Try these two at your seat without too much assistance!
x + 2y = 8
1
x – y = 18
2
5x + y = 6
3–x=0
Homework: A#
Chap 3 Sec 2 (con’t)
Pg 45
Solve a system of equations using ________________________________.
When we do this please follow these steps until you are confident in your steps!
Step 1: Multiply either equation (or both, possibly) by a constant so that the
coefficients are the same (but with opposite signs) for EITHER the first or the
second variable.
Step 2: _________ down to eliminate a variable.
Step 3: Solve for the remaining variable.
Step 4: Substitute the value found in Step 3 back into EITHER equation and solve
for the remaining unknown variable.
Let’s give it a try! Solve the system of equations 4a + 2b = 15 and 2a + 2b = 7.
Solve the system of equations: 6x + 3y = 6 and 8x + 5y = 12.
Chap 3 Sec 2 (con’t)
Pg 46
Try these two at your seat (I will do them on the board, so look up if you get
stuck).
3x – 2y = 12
2
2x + y = 14
3
3x – 4y = 12
1
4
4
x y
3
9
3
Homework: A#
(hint: multiply by the ___________________________________)
Algebra II Notes
Pg 47
Chapter 3 Section 3
Remember what you know about graphing inequalities from the previous
section. What do we recall?
We are going to do a few examples in class – I don’t think you will have too many
problems with this.
Solve the system of equations by graphing and give a point in the solution set if
there is one.
y > -2x + 4
y≤x–2
Pg 48
Solve the system of equations by graphing and give a point in the solution set if
there is one.
1
y > x 1
2
1
y< x3
2
Find the coordinates of the vertices of the figure formed by x + y ≤ -1,
x – y ≤ 6, and 12y + x ≤ 32.
Homework: A#
Algebra II Notes
Chapter 3 Section 5
Solve the 3 x 3 system of equations:
-4a = 8
4a + 2c = 0
7b + 3c = 22
x + y = -1
2x – y = -2
4x + y – z = 8
Pg 49
Pg 50
More often these types of problems will look like this one below!
Solve the 3 x 3 system of equations:
x + 2y + z = 10
2x – y + 3z = -5
2x – 3y – 5z = 27
Pg 51
Solve the 3 x 3 system of equations:
2x – y + z = 1
x + 2y – 4z = 3
4x + 3y – 7z = -8
Pg 52
Solve the 3 x 3 system of equations:
x + y + z = 12
6x – 2y – z = 16
3x + 4y + 2z = 28
Homework: A#