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Solving Word Problems Using Systems of Equations BY SAM SACCARECCIA

Solving Word Problems Using Systems of Equations BY SAM SACCARECCIA. Introduction. Directions. Lesson. Quiz. Introduction. Subject: Solving Word Problems by setting up a system of equations. Intended Learners: Tenth Grade

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Solving Word Problems Using Systems of Equations BY SAM SACCARECCIA

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  1. Solving Word Problems Using Systems of Equations BY SAM SACCARECCIA Introduction Directions Lesson Quiz

  2. Introduction Subject: Solving Word Problems by setting up a system of equations. Intended Learners: Tenth Grade Objective: To learn how to create a system of equations to solve complex word problems, meeting the benchmark for the Patterns, Functions and Algebra Standard

  3. QUIZ Question 1: A boat traveling against the current goes 276 miles in 3 hours. When it travels back against the current it goes 340 miles in only 2 hours. What is the boat’s speed in still water (no current) and what is the speed of the current? Boat -147mph Current-42mph Boat-131mphCurrent=39mph I Have No Idea……

  4. DIRECTIONS Use the links to navigate through the lesson. Upon completion there is a brief quiz to test your comprehension of the topic.

  5. HOORAY!!!! You are correct!!!! On to Question 2……

  6. Ooops that’s not correct….try again

  7. Sorry that’s incorrect try again….

  8. Question 2: A supersonic plane flies into a jet stream for 4 hours and travels 1308 miles. If the same jet then travels 4734 miles in 6 hours with the jet stream how fast is the plane flying without wind and what is the speed of the jet stream? Jet Stream-237mph Plane-1545mphJet Stream- 223mph Plane 1454mph

  9. FANTASTIC!!! The last question awaits…..

  10. Question 3: Another boat travels with the current for 5 hours and covers a distance of 400 miles. When it travels the same amount of time against the current it only travels 380 miles. How fast is the current and how fast would the boat be traveling without a current? Boat-76mph Current-2mphBoat-73mph Current-5

  11. Not quite but, you’re almost there…….

  12. Congratulations!! You Have Mastered Solving word Problems Using systems of equations!!!!

  13. LESSON Sometimes word problems require you to set up a system of equations in order to solve them. This lesson is designed to show you how to accomplish such a feat.

  14. Systems of Equations A system of equations is two equations for which there are exactly two values that solve both equations. One “x” value and one “y” value. Example: x+y= 13 x-y=1 For this example x=7 and y=6. This is because 7+6=13 and 7-6=1.

  15. We solve a system by first using one equation (preferably the easier one) to solve for one of our two variables. Using our example: x+y=13 x-y=1 First we take x-y=1 and solve for x. We accomplish this by adding y to both sides which gives us x=y+1

  16. Now that we know what x equals in terms of y (x=1+y), we can now solve our second equation using this value for x. x+y=13 Substituting in (x=1+y) gives us: (1+y)+y =13 This simplifies to: 1+2y=13 Subtract 1 from both sides: 2y=12 Divide by 2 y=6

  17. Now that we know that y=6, we can now use this value to solve for x: We know: x=1+y We also know: y=6 So: x=1+6 x=7 So the solution to our system is x=7 y=6

  18. Sometimes we need to use a system of equations to solve word problems. This is because there may not be enough information contained in the problem to solve it using only one equation. For example: A plane traveling with the wind covers a distance of 714 miles in 2 hours. Flying against the wind for 3 hours it only goes 531 miles. How fast would the plane be traveling with no wind? Also, how fast is the wind?

  19. First we need to set up our system: We’ll make “x” the speed of the plane, And “y” the speed of the wind. This will make our total speed traveling with the wind: x+y And our total speed traveling against the wind: x-y

  20. From here we need to know that distance traveled is equal to speed multiplied by time: For our first equation we know that the plane traveled with the wind for 2 hours and covered a distance of 714 miles. So we know that 2 multiplied by speed will give us 714 2(speed)=714 AND we know that our speed with the wind is x+y Thus: 2(x+y)=714

  21. Now for the second equation of our system we will use the given information about the plane traveling against the wind. We know that it traveled for 3 hours and covered a distance of 531 miles. We also decided that our speed against the wind is (x-y) So our second equation of our system is: 3(x-y)=531

  22. Now we have a system of equations which will allow us to solve for both x and y. 2(x+y)=714 3(x-y)=531 The next step is to solve one of these equations for x…. I’m going to use 3(x-y)=531because I think it is easier, but you may want to start with the other equation and that’s fine too.

  23. So to solve 3(x-y)=531 for x in terms of y, the first step is to divide both sides of the equation by 3*** This gives us: x-y= 177 Adding y to both sides gives us: x=177+y *** Notice you COULD distribute 3 to (x-y) which would give you 3x-3y=531 and you will still be able to find the right answer but it would give you more work to do and nobody wants that.

  24. Now that we have x=177+y we can substitute it into our second equation: 2(x+y)=714 After the substitution we have: 2[(177+y)+y]=714 We will divide both sides by 2 (Again you COULD distribute the 2 but trust me you don’t want to…) After dividing by 2 we get: 177+y+y=357 This simplifies to: 177+2y=357 Subtract 177 from both sides: 2y=180 Divide by 2 and: y=90

  25. No that we know our value of y we can find x, because we know that y=90 and x=177+y So we will substitute 90 in for y which gives us: x= 177+90 So x= 267 We have now determined the solution to our system y=90 x=267

  26. But wait there’s more!!!

  27. Remember that we were not asked to solve for x and y, we were asked to solve for the speed of the plane and the speed of the wind. x is the speed of the plane which equals 267mph y is the speed of the wind which equals 90mph OK. NOW you’re done. Now complete the brief quiz to demonstrate your comprehension.

  28. References Miller, Maria. Solving math word problems and setting up equations. Ed. Maria Miller. N.p., 2003. Web. 9 Feb. 2012. <http://www.homeschoolmath.net/teaching/teach-solve-word-problems.php>.

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