April 4, 2016

April 4, 2016

• 1.
  Today:  Warm-Up: Old& New  New Type of Systems Problem  Intro. to Systems of Inequalities  CW 4.1 - 4.2 due as of last Friday  Last day for Khan Academy is Tomorrow  CW 4.3 Distributed Tomorrow 4/04/16
• 2.
  The pie chartbelow shows how the average family spends their money while on vacation. If a family spent $3000 while on vacation, how much was spent on gas? What simplified fraction of the cost is spent on food and entertainment? Warm-Up: Review Questions
• 3.
  12 3 2  xy 4 3 4 1  xy Whatis y when x = -18 What is y when x = -6 Warm-Up: Review Questions
• 4.
  Is the systemconsistent or inconsistent? Is the system dependent or independent? Write the systems of equations shown on the graph. Warm-Up: Systems of Equations
• 5.
  For her birthday,Markbought his mom 12 flowers, a mixture of roses and daisies. The roses cost $1.15 each and the daisies cost $1.35 each. If he spent $16.00, how many daisies did he buy? x = y = # of roses # of daisies 12x y  1.15 1.35 16.00x y   100  100  100 115x 135y 1600 115x 12x y    12x  11 11 11  1x  11 daisies 1. Mark the text. 2. Label variables. 3. Create equations. 4. Solve. 5. Check.  115  115  115 115y 1380  20 20 11y  20 220y  Let’s eliminate the ‘x’ Try solving by elimination Warm-Up: Systems of Equations
• 6.
  A math testhas a total of 25 problems. Some problems are worth 2 points and some are worth 3 points. The whole test is worth 63 points. How many 2-point problems were there? x = y = # of 2-point problems # of 3-point problems 25x y  2 3 63x y   2  2  2 13y  2x 2y 50  2 3 63x y  25x y    25x  13 13 13  12x  12 2-point problems 1. Mark the text. 2. Label variables. 3. Create equations. 4. Solve. 5. Check.
• 7.
  Solving 3x3 Systems:(1) Thegraph of the solution set of an equation in three variables is a plane, not a line. In fact, graphing equations in three variables requires the use of a three-dimensional coordinate system. It is therefore, not practical to solve 3x3 systems by graphing Solve the System: 4x + 2y - z = -5 3y + z = -1 2z = 10 1. Which is the easiest variable to solve for? 2. Plug in where and solve for what? 3. Substitute y and z values into equation 1; solve for x. 4. Substitute all values, check for equality. 5. The solution set is (1, -2, 5) Solving 3x3 Systems:
• 8.
  A sporting goodsstore is having a sale on soccer equipment. One coach buys 10 soccer balls and 2 ball bags $155. Another coach buys 12 soccer balls and 3 ball bags for $189. What is the cost of each item? Write the equations and determine the best method for solving. Last warm-Up Question Write the equations and determine the best method for solving.
• 10.
  Many systems questionsask you to compare the costs of two different businesses like fitness clubs, car rentals, home repair, and then determine after how many months, miles, or hours, the costs will be the same. This question is asking after how many months will the cost be the same for both companies. Even though these are not solved by graphing, we still must determine the independent and dependent variables. The cost depends on the number of months used. The cost for Interwebs is..... What is the slope-intercept form of both equations?
• 11.
  After writing thetwo equations, what method is best for solving? y - 21.95x = 10 y - 22.45x = 0 1. Use elimination to solve for 'x', which is the number of months until the costs are equal. .5x = 10 x = 20 If you're only going to use an internet service for one year, which company would you choose? What is the cost for both companies after 20 months? 2. Use substitution to solve for 'x', which is the number of months until the costs are equal.
• 12.
  What are theindependent and dependent variables? Write the two equations and solve Write costs for both companies in slope intercept form. Rearrange into standard form.