1. 6.5 – Applying Systems of Linear Equations

2. Ex x + 4y = -25
2x – 3y = 6

3. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”

4. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x”

5. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x”

6. Ex [3x + 4y = -25]
-3[2x – 3y = 6]
Eliminate “x”

7. Ex [3x + 4y = -25]
-3[2x – 3y = 6]
Eliminate “x”
6x + 8y = -50
-6x +9y = -18

8. Ex [3x + 4y = -25]
-3[2x – 3y = 6]
Eliminate “x”
6x + 8y = -50
-6x +9y = -18

9. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x”
6x + 8y = -50
-6x +9y = -18
17y = -68

10. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x”
6x + 8y = -50
-6x +9y = y = -68

11. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x”
6x + 8y = -50
-6x +9y = y = -68
y = -4

12. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x”
6x + 8y = -50
-6x +9y = -18
17y = -68
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

13. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”
6x + 8y = -50
-6x +9y = -18
17y = -68
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

14. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”
6x + 8y = -50
-6x +9y = -18
17y = -68
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

15. Ex [3x + 4y = -25]
4[2x – 3y = 6]
Eliminate “x” OR Eliminate “y”
6x + 8y = -50
-6x +9y = -18
17y = -68
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

16. Ex [3x + 4y = -25]
4[2x – 3y = 6]
Eliminate “x” OR Eliminate “y”
6x + 8y = x + 12y = -75
-6x +9y = x – 12y = 24
17y = -68
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

17. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”
6x + 8y = x + 12y = -75
-6x +9y = x – 12y = 24
17y = x = -51
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

18. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”
6x + 8y = x + 12y = -75
-6x +9y = x – 12y = 24
17y = x = -51
y = -4
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

19. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”
6x + 8y = x + 12y = -75
-6x +9y = x – 12y = 24
17y = x = -51
y = x = -3
3x + 4y = -25
3x + 4(-4) = -25
3x – 16 = -25
3x = -9
x = -3
(-3, -4)

20. Ex x + 4y = -25
2x – 3y = 6
Eliminate “x” OR Eliminate “y”
6x + 8y = x + 12y = -75
-6x +9y = x – 12y = 24
17y = x = -51
y = x = -3
3x + 4y = x + 4y = -25
3x + 4(-4) = (-3) + 4y = -25
3x – 16 = y = -25
3x = y = -16
x = y = -4
(-3, -4)

21. Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12
x + 2y = 14

22. Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12
-4[ x + 2y = 14]

23. Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12
-4[ x + 2y = 14]
4x – 3y = 12

24. Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12
-4[ x + 2y = 14]
4x – 3y = 12
-4x – 8y = -56

25. Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12
-4[ x + 2y = 14]
4x – 3y = x – 3(4) = 12
-4x – 8y = x – 12 = 12
-11y = x = 24
y = x = 6
(6,4)

26. Ex.3 3x – 7y = -14
5x + 2y = 45

27. Ex x – 7y = -14
5x + 2y = 45
2[3x – 7y = -14] [3x – 7y = -14]
7[5x + 2y = 45] -3[5x + 2y = 45]
6x – 14y = x – 35y = -70
35x + 14y = x – 6y = -135
41x = y = -205
x = y = 5
3x – 7y = x – 7y = -14
3(7) – 7y = x – 7(5) = -14
21 – 7y = x – 35 = -14
-7y = x = 21
y = (7,5) x = 7