1. Bellwork1/26
Solve by Graphing:
x + 2y = 7 x + y = 1

2. 1st Change to y = mx + b x + y = 1 y = -x + 1 x + 2y = 7 x-x+2y=-x+7

3. y = -1/2x + 7/ y = -x + 1 Y
7/2 = 3 1/2 X
(-5,6)
Notice the intersection is not at 2 pts.

4. To be able to solve a system of equations by substitution….
Objective
To be able to solve a system of equations by substitution….

5. 1.) Solve by Substitution
y = 3x - 1
2x + y = 9 So…...
2x + (3x-1) = 9
5x - 1 = 9 (add 2x and 3x)
5x = 10 (add 1 to both sides)
x = 2 (divide both by 5)

6. 1.) Solve by Substitution
Since x = 2 We can now substitute it back in
y = 3x (the 1st equation)
y = 3(2) -1(put in the x value)
y = (solve for y)
y = (2,5) is the solution

7. 1.) Solve by Substitution
Or …. x = 2 We can substitute it in the other one
2x + y = 9 (the 2nd equation)
2(2) + y = 9(put in the x value)
4 + y = 9(subtract 4 from both)
y = (solve for y)

8. Graph y = 3x -1 & x + y = 9
2x+y=9 Y
y = 3x - 1 X
Solution= (2,5)

9. 2.) Solve by Substitution
2x + 3y = 7
y + 1 = x So…..
2(y+1) + 3y = 7
2y y = 7(distribute the 2)
5y + 2 = 7(Add 2y & 3y)
5y = 5 & y = 1(divide both by5)

10. 2.) Solve by Substitution
Since y = 1 We can now substitute it back in
y + 1 = x (the 2nd equation)
1 + 1 = x (put in the y value)
2 = x (solve for x)
(2,1) is the solution

11. Solve by Substitution y = 3x You try this one y + 4x = 28
First find what x or y equals
Then Substitute into the other equation.
You try this one

12. Solve by Substitution y = 3x y + 4x = 28 3x + 4x = 28 7x = 28 x = 4
Since x = 4
y = 3x
y = 3(4)
y = 12
solution (4,12)

13. 3.) Solve by Substitution
First solve for x or y
2x + 4y = 8
3x + 5y = 14
1st… 2x = -4y + 8 (Subtract 4y) x = -2y + 4 (Divide by 2)
Now substitute for x
3(-2y + 4) + 5y = 14

14. 3.) Solve by Substitution
3(-2y + 4) + 5y = 14
-6y y = 14
-y + 12 = 14
-y = 2 so…. y = -2

15. 3.) Solve by Substitution
Since y = -2 and x = -2y + 4
Then x = -2(-2) + 4
x = 4 + 4
x = 8
Solution (8,-2)

16. Classwork Do worksheet 7.2
You must use a separate sheet of paper to show the work!!!

17. Homework
Page 356 (1-4 all, 6-28 even)