1. Bellwork 1/27 Solve the following by:
y = 2x y = x ) Substitution 2.) Graphing (Use an old graph paper)

2. Bellwork 1/27 y = 2x y = x + 3 2x = x + 3 (Subtract x)
x = 3 and since y = 2x
y = 2(3)
y = Solution is (3,6)

3. Graph y = 2x & y = x + 3
y = x + 3 Y
y = 2x X
Solution= (3,6)

4. Bellwork 1/28 Solve the following by:
x - y = x + y = 1 1.) Substitution 2.) Graphing (Use an old graph paper)

5. Bellwork 1/28 x - y = 2 & 2x + y = 1 2x + y = 1 (Solve for y)
2x - 2x + y = -2x + 1
y = - 2x + 1
x - (-2x + 1) = 2 (Substitute)

6. Bellwork 1/28
x - (-2x + 1) = 2
x + 2x - 1 = 2
3x - 1 = 2
3x = 3
x = 1

7. Bellwork 1/28
y = - 2(1) + 1
y =
y = -1
Solution (1,-1)

8. Graph x - y = 2 & 2x + y = 1 y = x - 2 & y = -2x + 1
Solution= (1,-1)

9. Lets Graph this new equation
Check this out
Now Consider what happens when we add the two equations y = 2x y = x + 3
Lets Graph this new equation
2y = 3x + 3

10. How does this graph compare with the other two?
Graph 2y = 3x + 3 or y = 3/2x + 3/2 Y
How does this graph compare with the other two? X
y = 3/2x +3/2

11. Graph 2y = 3x + 3
y = -2/3x + 4 Y
y = 2x X
Notice that the graph passes thru the point of intersection
Solution= (3,6)

12. Objective
To be able to solve a system of equations by using the linear combination (add) method

13. 1.) Solve by Addition (elimination)
2x + 3y = 7
x - 3y = 8
(Divide by 3)
3x = 15
x = 5

14. 1.) Solve by Addition (elimination)
2x + 3y = 7 2(5) + 3y = 7
10 + 3y = 7
Solution (5,-1)
(Subtract 10)
3y = -3 (Divide by 3
y = -1

15. 2.) Solve by Addition (elimination)
3a = 2b + 7
2b = 9 - a
Notice that the like terms of the two equations do not line up.
3a - 2b = 7 a + 2b = 9
Rearrange them and THEN add

16. 2.) Solve by Addition (elimination)
3a - 2b = 7
a +2b = 9
(Divide by 4)
4a =
a = 4

17. 2.) Solve by Addition (elimination)
Now Substitute back into one of the equations
2b = 9 - a
2b = 9 -(4)
2b = 5
b = 5/2
Solution (4, 5/2)

18. 3.) You try This one
2x - y = 7
x+ y = 2
(Divide by 3)
3x = 9
x = 3

19. 3.) You try this one x + y = 2 (3) + y = 2 y = -1 (Subtract 3)
Solution (3,-1)

20. Be ready to answer
1.) What are the other two methods of solving two equations?
2.) What do you do, before you add, if the terms of the equation aren’t lined up?

21. Classwork
On a separate sheet of paper show the work for: Worksheet 7-3
Homework
Page 363 (1-16)

22. How many solutions do the following equations have?
1.) x = 3y
2x - y = 5
2.) 8x - 4y = -32
-2x + y = 8
One (3,1)
Many

23. How many solutions do the following equations have?
1.) y = 3x -2
3y + 2 = 9x
2.) y = 1/4x + 3
8y - 3x = 12
None
One (12,6)

24. 1.) y = 3x + 4 Graph y = mx + b Y-intercept Slope
Bellwork 1/31 (3 slides)
Graph
y = mx + b
1.) y = 3x + 4
Y-intercept
Slope
1 of 3

25. 2.) 2x + y = -1 Graph y = mx + b Y-intercept Slope
Bellwork 1/31 (3 slides)
Graph
y = mx + b
2.) 2x + y = -1
Y-intercept
Slope
2 of 3

26. 3.) -2x - y = - 5 Graph y = mx + b Y-intercept Slope
Bellwork 1/31 (2 slides)
Graph
y = mx + b
3.) -2x - y = - 5
Y-intercept
Slope
3 of 3

27. Graph y = 3x + 4 Y X

28. Graph 2x + y = -1 y = -2x + -1 Y X

29. Graph -2x - y = -5 y = -2x + 5 Y X

30. Classwork Solve the following by: y = 2x y = x + 3 1.) Graphing
2.) Substitution
3.) Linear Combination (+)
Show all your Work

31. Graph y = 2x & y = x + 3
y = x + 3 Y
y = 2x X
Solution= (3,6)

32. Classwork (Sub) y = 2x y = x + 3 2x = x + 3 (Subtract x)
x = 3 and since y = 2x
y = 2(3)
y = Solution is (3,6)

33. Classwork (L.C.) y = 2x y = x + 3 (multiply by -1) -y = -x - 3
y = 2x(rewrite 1st equation & add)
0 = x - 3 (Add the equations)
x = 3

34. Classwork (L.C.)
Since x = 3, then
y = 2(3)
y = 6
Solution ( 3,6)

35. Classwork (1 of 3) Solve the following by: y = -x + 3 y = x + 1
1.) Graphing
2.) Substitution
3.) Linear Combination (+)
Show all your Work

36. Classwork (2 of 3) Solve the following by: 3x - y = 0 y = 6
1.) Graphing
2.) Substitution
3.) Linear Combination (+)
Show all your Work

37. Classwork (3 of 3) Solve the following by: x - y = 4 x + y = 12
1.) Graphing
2.) Substitution
3.) Linear Combination (+)
Show all your Work

38. Classwork
1 of 3) (1 , 2)
2 of 3) (2 , 6)
3 of 3) (8 , 4)

39. Homework
Page 373 (2-20 even)