complete the do now in your packets. solving systems of equations by graphing name: pd algebra...
TRANSCRIPT
• Complete the DO NOW in your packets
Solving Systems of Equations by Graphing
Name: Pd
Algebra 2/26/09
System of Linear
Equations: y = 2/5x – 2 y = -3x + 15{
Solution to a System of Linear Equations:
Solution (5, 0)
2/5(5) – 2 = 0 -3(5) + 15 = 0{
x, y
having more than one linear equation.
is the ordered pair or pairs that satisfy all equations.
Three ways to solve a system of equations:
Graphing
Elimination
Substitution
y = 2/5x – 2 y = -3x + 15{
5x + 3y = 3 2x – y = 6 {
4x – 3y = 6 y = -3x + 15{
There are three possible outcomes for the solutionsof a system:
One Solution
No Solution
Infinite Solutions
(1, 1)
(0, -3)
(-1, 2) (1, 4)
Ex1: Find the solution to the given system by graphing.
y = -1x + 3y = 1/2x – 3{
Solution: (4, -1)
y = 2x – 5y = -3/2x + 2{
Solution: (2, -1)
Ex2: Find the solution to the given system by graphing.
y = -5y = -4x + 3{
Solution: (2, -5)
Ex3: Find the solution to the given system by graphing.
y = -1/2x + 3y = -1/2x – 1 {
No Solution
Ex4: Find the solution to the given system by graphing.
Ex5: Find the solution to the systems by graphing.
2x + 6y = -12 4x – 4y = -8 {
2x + 6y = -12-2x -2x
6y = -12 – 2x 6 6y = -2 –1/3x
4x – 4y = -8 -4x -4x
-4y = -8 – 4x -4 -4
y = 2 + x
Solution (-3, -1)
Ex6: Find the solution to the systems by graphing.
-4x + 8y = 16 6x – 3y = 12{
-4x + 8y = 16+4x +4x
8y = 16 + 4x 8 8y = 2 + 1/2x
6x – 3y = 12 -4x -6x
-3y = 12 – 6x -3 -3
y = -4 + 2x
Solution (4, 4)
Ex7: Find the solution to the systems by graphing.
{
x – y = 4 -1x -1x
-1y =-1x + 4 -1 -1 -1y = 1x – 4
-5x + 5y = -20 +5x +5x
5y = 5x – 20 5 5 5
y = 1x – 4
Infinite Solutions
x – y = 4 -5x + 5y = -20
• No homework tonight!
• Finish your packets to be collected at the end of the hour
• Tomorrow we will continue with solving systems of equations by graphing.