1. HW: Maintenance Sheet #21 (19-21) comprehensive Test 7 Friday
No talking
Practice Quiz:
Place in folder and
answer questions 7-8
Coming soon, April 13
Let’s
Whip that
test

2. Homework Check 9-18

3. I can solve and explain (in terms of the situation) a system of linear equations graphically, including those that have no solution or infinitely many solutions.
I can solve and explain (in terms of the situation) a system of linear equations algebraically, including those that have no solution or infinitely many solutions.
I can solve real-world problems involving a system of linear equations.
Systems of Equations
MCC8.EE.8 Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

4. Station Rules Work with a partner
Keep your voices low and only about MATH.
Utilize all resources
READ YOUR DIRECTIONS CAREFULLY!
DO NOT WRITE ON HANDOUTS!

5. Solve using the following system.
2x – 3y = 1
x + 2y = -3
(2, 1)
(1, -2)
(5, 3)
(-1, -1)

6. Solving Systems of Equations
Three ways to solve systems of equations.
graphing, substitution, and elimination.
Today, we will learn about ELIMINATION
What does it mean to eliminate something?

7. Elimination Video

8. What is the first step when solving with elimination?
Add or subtract the equations.
Multiply the equations.
Plug numbers into the equation.
Solve for a variable.
Check your answer.
Determine which variable to eliminate.
Put the equations in standard form.

9. Which variable is easier to eliminate?
3x + y = 4
4x + 4y = 6 x y 6 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

10. Elimination
4x+3y = -6 2x-3y = 24

11. 1) Solve the system using elimination.
2x + 2y = 6
3x – y = 5
Step 1: Put the equations in Standard Form.
They already are!
None of the coefficients are the same!
Find the least common multiple of each variable.
LCM = 6x, LCM = 2y
Which is easier to obtain?
2y (you only have to multiply the bottom equation by 2)
Step 2: Determine which variable to eliminate.

12. 1) Solve the system using elimination.
2x + 2y = 6
3x – y = 5
Multiply the bottom equation by 2
2x + 2y = 6
(2)(3x – y = 5)
8x = 16
x = 2
2x + 2y = 6
(+) 6x – 2y = 10
Step 3: Multiply the equations and solve.
2(2) + 2y = 6
4 + 2y = 6
2y = 2
y = 1
Step 4: Plug back in to find the other variable.

13. 1) Solve the system using elimination.
2x + 2y = 6
3x – y = 5
(2, 1)
2(2) + 2(1) = 6
3(2) - (1) = 5
Step 5: Check your solution.
Solving with multiplication adds one more step to the elimination process.

14. 2) Solve the system using elimination.
x + 4y = 7
4x – 3y = 9
Step 1: Put the equations in Standard Form.
They already are!
Find the least common multiple of each variable.
LCM = 4x, LCM = 12y
Which is easier to obtain?
4x (you only have to multiply the top equation by -4 to make them inverses)
Step 2: Determine which variable to eliminate.

15. 2) Solve the system using elimination.
x + 4y = 7
4x – 3y = 9
Multiply the top equation by -4
(-4)(x + 4y = 7)
4x – 3y = 9)
y = 1
-4x – 16y = -28
(+) 4x – 3y = 9
Step 3: Multiply the equations and solve.
-19y = -19
x + 4(1) = 7
x + 4 = 7
x = 3
Step 4: Plug back in to find the other variable.

16. 2) Solve the system using elimination.
x + 4y = 7
4x – 3y = 9
(3, 1)
(3) + 4(1) = 7
4(3) - 3(1) = 9
Step 5: Check your solution.

17. 3) Solve the system using elimination.
3x + 4y = -1
4x – 3y = 7
Step 1: Put the equations in Standard Form.
They already are!
Find the least common multiple of each variable.
LCM = 12x, LCM = 12y
Which is easier to obtain?
Either! I’ll pick y because the signs are already opposite.
Step 2: Determine which variable to eliminate.

18. 3) Solve the system using elimination.
3x + 4y = -1
4x – 3y = 7
Multiply both equations
(3)(3x + 4y = -1)
(4)(4x – 3y = 7)
x = 1
9x + 12y = -3
(+) 16x – 12y = 28
Step 3: Multiply the equations and solve.
25x = 25
3(1) + 4y = -1
3 + 4y = -1
4y = -4
y = -1
Step 4: Plug back in to find the other variable.

19. 3) Solve the system using elimination.
3x + 4y = -1
4x – 3y = 7
(1, -1)
3(1) + 4(-1) = -1
4(1) - 3(-1) = 7
Step 5: Check your solution.

20. What is the best number to multiply the top equation by to eliminate the x’s?
3x + y = 4
6x + 4y = 6 -4 -2 2 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

21. Solving Systems with Algebra graphic organizer
Example 2
2x+5y = 14
4x + 2y = -4

22. Solving Systems with Algebra graphic organizer
Example 3
3x-4y = -37
-5x + 3y = 14

23. TOD: Solving Systems with Algebra graphic organizer
a. X – 3y = 7 2x – 6y = 12 b. -5x + 15y = -30