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March 28, 2016
- 1. Today: 4th QuarterGrade Trackers Make-Up Tests? --Today @ Lunch only Systems of Equations 1st & 3rd Periods: Leave Notebooks 4th & 5th Periods, Tomorrow CW 4.1 Distributed Today March 28, 2016
- 8. Is it independentor dependent? Is it consistent or inconsistent? Is it independent or dependent? Is it consistent or inconsistent?
- 9. Determine whether theordered pair is a solution of the given system. The ordered pair (5, 2) makes both equations true. (5, 2) is the solution of the system. Substitute 5 for x and 2 for y in each equation in the system. 2 – 2 0 0 0 0 3(5) – 2 13 15 – 2 13 13 13 3x – y 13 (5, 2); 3x – y = 13 𝟐 𝟓 x – y = 0 𝟐 𝟓 x – y = 0
- 10. –2 + 3(2)4 x + 3y = 4 –2 + 6 4 4 4 –x + y = 2 – (–2) + 2 2 4 2 (–2, 2) is not a solution of the system. If an ordered pair does not satisfy the first equation in the system, there is no reason to check the other equation(s). Helpful Hint Determine whether the ordered pair is a solution of the given system.
- 11. SOLVING SYSTEMS BYELIMINATION: 1. Arrange the like variables in columns. 2. Pick a variable, x or y, and make the two equations opposites using multiplication. 3. Add the equations together (eliminating a variable) and solve for the remaining variable. 4. Substitute the answer into one of the ORIGINAL equations and solve. 5. Check your solution. (BY ADDITION OR SUBTRACTION)
- 12. 5x - 4y= -21 -2x + 4y = 18 We need to eliminate (get rid of) a variable by cancelling out one of the variables. We then solve for the other variable. 3x + 0 = -3 x = -1 THEN---- Like variables must be lined under each other. What should we eliminate first? Solve: By Elimination Do we add or subtract the two equations?
- 13. 5x - 4y= -21 (-1, 4) Substitute your first solution into either original equation and solve for the second variable. The solution to this system of equations is: Now check your answers in both equations------ 5(-1) – 4y = -21 -5 – 4y = -21 5 5 -4y = -16 y = 4
- 14. 5x - 4y= -21 5(-1) – 4(4) = -21 -5 - 16 = -21 -21 = -21 -2x + 4y = 18 -2(-1) + 4(4) = 18 2 + 16 = 18 18 = 18
- 15. 5x + 4y= -21 -2x + 4y = 18 Solve: By Elimination This system is nearly identical to the previous example with one difference. How must we proceed?
- 16. We have twooptions; what are they? 3x + y = 29 x + 4y = 6 We need to eliminate (get rid of) a variable. To simply add this time will not eliminate a variable. a. Subtract b. Multiply one of the equations by -1, then add SOLVING SYSTEMS BY ELIMINATION: (BY MULTIPLICATION)
- 17. 3x + y= 29 x + 4y = 6( ) - 3x + 12y = 18 Now subtract the two equations and solve. -11y = 11 - 11 - 11 y = - 1 THEN---- 3x + y = 29 Substitute your answer into either original equation and solve for the second variable.
- 18. 2x - 5y= 2 -3x + 2y = -14
- 20. Which of thetwo equations would be the easiest for isolating a variable? SOLVING SYSTEMS BY SUBSTITUTION:
- 21. SOLVING SYSTEMS BYSUBSTITUTION: 1. Isolate (solve) one of the equations for x or y. 2. Substitute your new expression from Step 1 into the other equation and solve for the variable. 3. Plug that solved variable into the other equation from Step 1 and solve for the other variable. 4. Check your answers by plugging it into the original equations. - Get x or y by itself.
- 22. SOLVING SYSTEMS BYSUBSTITUTION:
- 24. SOLVING SYSTEMS WORDPROBLEMS: Kelly went back-to-school shopping this weekend. She spent $160 on jeans and shirts. She bought a total of 12 items, with jeans costing $16 and shirts costing $12. How many jeans and shirts did she buy? 1. Mark the text. 2. Label variables. j = jeans s = shirts 3. Create equations. 16j + 12s = 160 What’s the 2nd equation?j + s = 12 4. Solve. 5. Check.
- 25. Mrs. Smith tookher family and friends to the movies. There were a total of 12 people. Children tickets cost $5 and adult tickets cost $10. She spent a total of $95. How many adults & how many children went to the movies? 1. Mark the text. 2. Label variables. 3. Create equations. 4. Solve. 5. Check.