Download Concepts 1.1

Bell Work
1/28/15
Graph the equation.
1.
y  2x  3
2.
3
y   x 1
2
Yesterday’s Homework
1. Any questions?
2. Please pass your homework to the front.
• Make sure the correct heading is on your paper.
• Is your NAME on your paper?
• Make sure the homework is 100% complete.
• Incomplete work will NOT be accepted.
Next Chapter
Chapter 6
Systems of Equations
and Inequalities
Heading
5/24/2017
6.1A Solving Systems by
Graphing (y = mx+b)
TSWBAT: solve a linear system by
graphing when in slope-intercept
form.
Students solve a system of two linear equations in
two variables algebraically and are able to interpret
the answer graphically. Students are able to solve a
system of two linear inequalities in two variables
and to sketch the solution sets.
Notes
• Definitions
• Linear System (or System of Equations)
= Two or more equations with the same variables
2 x  3 y  2
Ex. 
5 x  4 y  1
• Solution of a Linear System
= The point where the two lines cross/intersect.
-Must make BOTH equations TRUE!
• Point of Intersection
= The solution of the linear system.
Notes
• Solving a System of Equations by Graphing
1. Write each equation into slope-intercept form.
y  mx  b
m  slope
b  y - intercept
What is m and b?
m = move
b = beginning
2. Graph both equations in the same coordinate plane.
3. Find the point of intersection.
4. Check your answer.
- Plug that point into both equations and
make sure that it is true for both.
Notes
Solve the system by graphing.
Ex.
2
 y  2 x  3 m   1 b  3

3
y

3
x

7

m
b  7
1
1) Put in slopeintercept form.
2) Graph the
equations.
 2,  1
- Find m
and b first.
3) Point of
intersection?
4) Check
answer!
Notes
Step 5- Check your answer.
 2,  1
x
y
y  2 x  3
y  3x 7
1  2  2   3
1  3 2   7
1  4  3
1  1
1  6  7
1  1
 2,  1
Notes
Solve the system by graphing.
Ex.
4
m
 y  4x 1
1

2
y


2
x

5

m
1
Now you try.
b 1
b  5
1) Put in slopeintercept form.
2) Graph the
equations.
 1,  3
- Find m
and b first.
3) Point of
intersection?
4) Check
answer!
Notes
Step 5- Check your answer.
 1,  3
x
y
y  4x 1
y  2 x  5
3  4 1 1
3  2 1  5
3  2  5
3  3
3  4 1
3  3
 1,  3
Notes
Solve the system by graphing.
Ex.
1
m
b  3
1

2
y

x

3

3
2
m
b5

2
3
1) Put in slopeintercept form.
y   x  5

2
2) Graph the
equations.
 4,  1
- Find m
and b first.
3) Point of
intersection?
4) Check
answer!
Notes
Step 5- Check your answer.
 4,  1
1
y  x3
2
1
1   4   3
2
1  2  3
1  1
x
y
 4,  1
3
y   x5
2
3
1    4   5
2
1  6  5
1  1
Notes
Solve the system by graphing.
Ex.
5
m
b  7
5

3
y


x

7

1
3
m

b6

2
1
y  x  6

2
Now you try.
1) Put in slopeintercept form.
2) Graph the
equations.
 6, 3
- Find m
and b first.
3) Point of
intersection?
4) Check
answer!
Notes
Step 5- Check your answer.
 6, 3
5
y   x7
3
5
 3    6  7
3
3  10  7
33
x
y
 6, 3
1
y  x6
2
1
 3   6  6
2
3  3  6
33
Notes
• Number of Solutions for a Linear System
A
B
C
One solution
No solution
Infinite solutions
(Same Lines)
(Parallel Lines)
0#
00
Notes
Solve the system by graphing.
Ex.
2
m
b4
2

3
y

x

4

2
3
m
b  1

3
2
 y  x 1

3
1) Put in slopeintercept form.
2) Graph the
equations.
No Solution
- Find m
and b first.
3) Point of
intersection?
4) Check
answer!
Summary
graphing first
To solve a linear system by ________
graph each equation separately. Next identify the
intersection
__________ of both lines and circle it. That ordered
solution to the system. Check your answer
pair is the _______
system of equations.
by plugging it back into the ______
Today’s Homework
Rules for Homework
1. Pencil ONLY.
2. Must show all of your work.
• NO WORK = NO CREDIT
3. Must attempt EVERY problem.
4. Always check your answers.
Homework
6.1A
Solve the system by graphing.
 y  2x  3
 y  4 x  1
1.
2.


 y  3x  2
 y  2x  5
4.
2

y

x 1

3

y   1 x  2

3
7.
1

y

x4

3

y  1 x  2

3
5.
3

 y   2 x  3

y  1 x  4

4
8.
 y  3x  4

y  x  4
3.
 y  3x  4

 y  2 x  6
6.
3

 y  2 x  5

y   2 x 8

3
9.
 y  3x  2

 y  3x  2
Ticket Out the Door
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Solve the system by graphing.
 y  2 x  1

 y  4x  7