1. Solving Systems of Equations The Substitution Method When will the substitution method be useful?

2. Solving Systems of Equations Substitution is often used when the equation is already solved for one variable or you have a problem that involves a fractional or large answer.

3. HERES A LITTLE DOG Solve the system of equations: 4y = -x + 7 y = 3/2x + 4

4. ANSWER (-9/7, 29/14)

5. Substitution Solve the system of equations x = 5 y = 2x + 3 REMEMBER: We are trying to find the point of Intersection. (x, y) Substitution is desired if one variable is already by itself or can be solved for very easily. What is already by itself on one side of the equation? So take x = 5 and plug it in for x in the other equation. y = 2(5) + 3 y = 10 + 3 y = 13 so (5, 13)

6. Substitution Solve the system of equations x = ⅙ y = ⅜ x – 4.2 REMEMBER: We are trying to find the point of Intersection. (x, y) Substitution is desired if one variable is already by itself or can be solved for very easily. What is already by itself on one side of the equation? So take x = ⅙ and plug it in for x in the other equation. y = ⅜ ( ⅙ ) – 4.2 y = 0.0625 – 4.2 y = -4.1375 so ( ⅙, -4.1375)

7. SOLVE USING SUBSTITUTION x = -17 y = -2x – 11 (-17, 23)

8. SOLVE USING SUBSTITUTION x = -2¼ y = 3x – ⅘ (-2¼, -7.55)

9. SOLVE USING SUBSTITUTION y + 105x = 254 y = 44 (2, 44)

10. SOLVE USING SUBSTITUTION y +½x = ⅞ y = ¼ (1.25, ¼)

11. YOU WRITE A PROBLEM One variable should already be isolated like x = -2 or y = 7 and the other should be in slope-intercept form. We will work some on the board.

12. Substitution Solve the system of equations y = x + 1 y = 2x - 1 REMEMBER: We are trying to find the Point of Intersection. (x, y) Substitution or graphing could work here but let’s use substitution. So take both equations and set them equal to each other since both equal y. x + 1 = 2x – 1 -2x -1x + 1 = – 1 - 1 - 1 -1x = -2 or x = 2

13. Substitution Consider the system y = x + 1 y = 2x - 1 REMEMBER: We are trying to find the Point of Intersection. (x, y) Now that you’ve found the answer for x = 2, how do you think you’ll find the answer for y? So what you got for x and plug it in and find y. You’ll now have your point of intersection. y = x + 1 y = 2 + 1 y = 3 Your answer is (2,3)

14. Substitution Consider the system of equations y = -1.5x y = -4x – 10 REMEMBER: We are trying to find the Point of Intersection. (x, y) Substitution or graphing could work. What is your final answer?(-4,6)

15. Substitution Consider the system of equations x + 2y = -1 4x - 4y = 20 REMEMBER: We are trying to find the Point of Intersection. (x, y) Substitution or graphing?. What is your final answer?(3,-2)

16. PRACTICE PROBLEMS PAGE 340 1-4, 18, 24

17. BIG DOG Solve the following systems of equations: 2x + 3y + 2z = 18 -4y + y – z = 5 2z = -10

18. ANSWER Solve the following systems of equations: 2x + 3y + 2z = 18 -4y + y – z = 5 2z = -10(2, 8, -5)