February 18, 2015
- 1. Today: Khan Academy Due Tonight Class Work: Show Your Work for Credit
- 3. Review Systems of Equations: Elimination (3) 2x + 4y = 16 4x - 4y = -4 There are 3 methods to solving by elimination. The problem will determine what method is used. A) Solve by addition or subtraction. If the coefficients of one of the variables are the same, that variable can easily be eliminated. 1) If the signs are different, add. 2) If the signs are the same, subtract. (Or multiply one of the equations by – 1, then add.) Solve the system of equations:
- 4. Review Systems of Equations: Elimination -2x - 5y = -4 6x + 15y = 12 There are 3 methods to solving by elimination. The problem will determine what method is used. B) Solve by multiplying one of the equations. Solve the system of equations: If the coefficient of one of the variables goes evenly into the other coefficient, then multiply every term by the number which makes the coefficients the same. Multiply by a negative number if the signs are currently the same.
- 5. Review Systems of Equations: Elimination 5x - 2y = 7 -3x - 5y = 2 There are 3 methods to solving by elimination. The problem will determine what method is used. C) Solve by multiplying both of the equations. Solve the system of equations: If none of the coefficients are factors of the other, then select a variable and find the LCM of the two coefficients. One of the equations may have to be multiplied by a negative number to make the signs different.
- 6. Review Systems of Equations: Substitution (2) x = - 3y - 4 2x + 5y = - 6 With substitution, we are trying to rearrange an equation to say y = .... or x = .... You have many options. Choose the easiest variable to solve for. We then take out the x or y in the other equation, and replace it with the right side of the equation we just solved for. Solve the system of equations by substitution: We then have one equation with one variable to solve for. After solving for the first variable, plug it back into the 2nd equation, and solve for the remaining variable. 2x - 4y = 12 x - 3y = 11 For this system, you must rearrange one of the equations to solve for x or y Which variable is the easiest to solve for?
- 7. Applying Systems of Equations: Prom tickets cost $10 for singles and $15 for couples. Fifty more couples tickets were sold than were singles tickets. Total ticket sales were $4000. How many of each ticket type were sold?
- 8. Solving Systems of Inequalities (2) Practice 1. Find the solution to: x + y < 1; x - y > 1 1: Rewrite in slope-intercept form: x - y > 1; 2: Graph the first line. 3: Lightly shade the correct side of the line. 4: Repeat steps 2 & 3 for the 2nd line. 5: Heavily shade the overlapping areas, which is the solution. x + y < 1; y < x - 1 y < -x + 1
- 9. Write the system of inequalities that produced this graph.
- 10. The sum of three numbers is 14. The largest is 4 times the smallest. The sum of the smallest and two times the largest is 18. Find the numbers. ( In the form (smallest, middle, largest number)). Solving a 3x3 System of Equations (1) x + y + z = 14 z = 4xx + 2z = 18 How many solutions does the system have: 12x - 8y = 20 3x - 2y = 5 How many solutions does the system have: Which point is a solution to the following system? 2y – x > - 6 2y – 3x < - 6 A) (- 4, - 1) B) (3, 1) C) (0, - 3) D) (4, 3) E) None x y z Solve by SubstitutionOther Problems (3)
- 11. Changes to Class Work 3.4: A) Do not do Systems of Inequalities #3 B) Make the following changes: