1. Unit 8 – Systems of Equations.
System of Equation - more than one equation that is solved by 1) graphing or 2) substitution Graphing is easier, but the answers are hard to find Substitution is harder, but the answers are exact

2. 3 types of answers A system has more than one equation for a problem.
The solutions are either
1) One solution, an ordered pair (x, y)
2) no solutions, parallel line
3) infinite solutions, same line

3. LT 8-1 I can determine if an ordered pair is a solution of a system of equations
4x – y = 10 2x – y = 6 Is (2, -2) a solution of the system? 4(2) – (-2) = 10 2(2) – (-2)= = 10 True = 6 True Yes it is

4. Is (3, 6) a solution of the system?
3x -2y = 6 x = 3
3(3) -2(6) = 6 x = 3
9 -12 ≠ 6 False
No cannot be a solution

5. Y = x – y + 3x = 33
Is (12, 3) a solution of the system? 3 = 1 4 (12) – (3) + 3(12) = 33 True True It is a solution

6. LT 8.3 I can solve a system of equations by substitution

7. Substitution Examples – just watch the process
y = -2x – 3 y = 2x + 5
-2x – 3 = 2x + 5
- 3 = 4x + 5
-8 = 4x so x = -2
y = 2(-2) + 5 = 1
Solution is ( -2, 1), check in the other equation = -2(-2) – 3 is true

8. Substitution
Step 1 - If both equations = the same value (usually y), set them equal to each other and solve
Step 2 – If not, solve one or both equations for a single variable and substitute in the other

9. 2. y = -x y = 3x - 5
-x + 7 = 3x – 5 7 = 4x – 5 12 = 4x 3 = x y = 3(3) – 5 = 4 Solution is ( 3, 4) check in the other equation 4 = -(3) + 7 is true

10. 5x -4(-3x + 5) = -3 Substitute for y
5x – 4y = -3 y = -3x + 5
5x -4(-3x + 5) = -3 Substitute for y
5x + 12x -20 = -3
17x – 20 = -3
17x = 17 x = 1
Find y y = -3(1) y = 2
Solution is (1, 2), check in 5(1) – 4(2) = True

11. y = 3x y = 3x + 4
3x = 3x = 4 not true No Solutions

12. 2y = 6x y - 2x = 1
Find the equation with a single variable and solve y - 2x = 1 y = 2x + 1 sub in for y in the red equation 2(2x + 1) = 6x + 2 4x + 2 = 6x = 2x = 2x x = 0 y = 2(0)+ 1 y = 1 (0,1)

13. LT 8.4 I can write and solve a system of equations.
3 steps
Define two variables
Write two equations
Solve the system

14. Example

15. Step 1 a = adult c = children Step 2 a + c = 7 c + 1 = a Step 3 (c+ 1) + c = 7 2c + 1 = 7 2c = 6 c = 3 3 children and 1 adult