HW: Study for Comprehensive Test #7 9. B 10. A No talking Practice Quiz: Place in Binder and answer questions 9-10 Coming soon, April 13 The correct answer is Choice (A) Students who play 4 sports are more likely to spend 2 to 5 hours on homework than students who play 1 sport because the relative frequency of 4 sports and 2 to 5 hours of homework is greater than the relative frequency of 1 sport and 2 to 5 hours of homework. The relative frequency of 4 sports in this category is (6 ÷14)× 100 = 42.9% and the relative frequency of 1 sport in this category is (6 ÷ 18) x100 = 33.3%. Let’s Whip that test

Homework Check 19-22 19. (-1,2) 20. D 21. 7.47 x 10-4 22. 5

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.

Independent Practice READ YOUR DIRECTIONS CAREFULLY! Work by yourself Utilize all resources (math notes) Visit the following videos if you still don’t understand from your notes. Graphing Video: http://tinyurl.com/KAgraphing Substitution Video: http://tinyurl.com/KAsubstitution Elimination Video: http://tinyurl.com/KAeliminaton

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

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?

Elimination Video

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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