You should always include a detailed self-critique when your solution doesn't completely agree with the given solution. Without the self-critique I can't tell what you did and did not understand about the solution and I have no way of helping you address anything you might not understand.

You do appear to have a good basis for understanding these procedures. Review the entire document and take some notes, and I think you'll be OK.

Let me know if you have specific questions on any of these ideas.

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11:54:31 `q001. Note that this assignment has 10 questions Solve the following system of simultaneous linear equations: 3a + 3b = 9 6a + 5b = 16.

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RESPONSE --> 3a + (5-3b) =9 6a + (3-5b) = 16 3a = 9 6b = 16 a = 3 b = 2.666 3(9) + 3b = 9 6(2.666) +5b = 16 27 +3b =9 15.996 + 5b = 16 3b = (9-27) 5b = (16 - 15.996) b = -18 b = 0.004

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11:56:17 The system 3a + 3b = 9 6a + 5b = 16 can be solved by adding an appropriate multiple of one equation in order to eliminate one of the variables. Since the coefficient of a in the second equation (the coefficient of a in the second equation is 6)) is double that in the first (the coefficient of a in the first equation is 3), we can multiply the first equation by -2 in order to make the coefficients of a equal and opposite: -2 * [ 3a + 3b ] = -2 [ 9 ] 6a + 5b = 16 gives us -6a - 6 b = -18 6a + 5b = 16 . Adding the two equations together we obtain -b = -2, or just b = 2. Substituting b = 2 into the first equation we obtain 3 a + 3(2) = 9, or 3 a + 6 = 9 so that 3 a = 3 and a = 1. Our solution is therefore a = 1, b = 2. This solution is verified by substituting these values into the second equation, where we get 6 * 1 + 5 * 2 = 6 + 10 = 16.

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RESPONSE --> I was confused and used another type of formule...I havent had math in awhile

Among other things this is intended as a bit of a refresher.

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12:01:36 `q002. Solve the following system of simultaneous linear equations using the method of elimination: 4a + 5b = 18 6a + 9b = 30.

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RESPONSE --> 6 * 4a + 5b = 18 -4 * 6a + 9b = 30 24a + 30b = 108 -24a + -36b = -120 -6b = -12 b = 2 4a + 5(2) = 18 4a = 8 a = 2 4*2 + 5*2 = 18 6*2 + 9*2 = 30

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12:02:35 In the system 4a + 5b = 18 6a + 9b = 30 we see that the coefficients of b are relatively prime and so have a least common multiple equal to 5 * 9, whereas the coefficients 4 and 6 of a have a least common multiple of 12. We could therefore 'match' the coefficients of a and b by multiplying the first equation by 9 in the second by -5 in order to eliminate b, or by multiplying the first equation by 3 and the second by -2 in order to eliminate a. Choosing the latter in order to keep the number smaller, we obtain 3 * [4a + 5b ] = 3 * 18 -2 * [ 6a + 9b ] = -2 * 30, or 12 a + 15 b = 54 -12 a - 18 b = -60. Adding the two we get -3 b = -6, so b = 2. Substituting this value into the first equation we obtain 4 a + 5 * 2 = 18, or 4 a + 10 = 18, which we easily solve to obtain a = 2. Substituting this value of a into the second equation we obtain 6 * 2 + 9 * 2 = 30, which verifies our solution.

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RESPONSE --> I didnt use the same coefficients but my answer was the same...did I do this correctly

You certainly did. There is usually more than one way to do the elimination.

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12:03:44 `q003. If y = 5x + 8, then for what value of x will we have y = 13?

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RESPONSE --> y = 13 13 = 5x + 8 13-8 = 5x 5 = 5x x = 1

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12:03:54 We first substitute y = 13 into the equation y = 5 x + 8 to obtain 13 = 5 x + 8. Subtracting 8 from both equations and reversing the equality we obtain 5 x = 5, which we easily solve to obtain x = 1.

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RESPONSE --> ok I usderstand

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12:09:03 `q004. Sketch a set of coordinate axes representing y vs. x, with y on the vertical axis and x on the horizontal axis, and plot the points (1, -2), (3, 5) and (7, 8). Sketch a smooth curve passing through these three points. On your curve, what are the y coordinates corresponding to x coordinates 1, 3, 5 and 7? Estimate these coordinates as accurately as you can from your graph. Retain your sketch for use in future assignments.

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RESPONSE --> the y corrdinates responding to the x coordinates of 1, 3, 5, and 7 are: 2.5 5, 7.4, 8.5

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12:09:39 The x coordinates 1, 3 and 7 match the x coordinates of the three given points, the y coordinates will be the y coordinates -2, 3 and 8, respectively, of those points. At x = 5 the precise value of x, for a perfect parabola, would be 8 1/3, or about 8.333. Drawn with complete accuracy a parabola through these points will peak between x = 3 in and x = 7, though unless you have a very fine sense of the shape of a parabola your sketch might well peak somewhere to the right of x = 7. The peak of the actual parabola will occur close to x = 6, and the value at x = 7 will be just a bit greater than 8, perhaps 8.5 or so. If your peak was to the right of x = 7, your x = 5 value will be lass than 7.

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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. ok

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12:11:50 `q005. Using your sketch from the preceding exercise, estimate the x coordinates corresponding to y coordinates 1, 3, 5 and 7. Also estimate the x values at which y is 0.

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RESPONSE --> the x coordinates are : 0.7 at y when 0 for 1, 3, 5, and 7 they are: 0.5, 1.2, 2, and 4

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12:12:07 The easiest way to estimate your points would be to make horizontal lines on your graph at y = 1, 3, 5 and 7. You would easily locate the points were these lines intersect your graph, then estimate the x coordinates of these points. For the actual parabola passing through the given points, y will be 1 when x = 1.7 (and also, if your graph extended that far, near x = 10). y = 3 near x = 2.3 (and near x = 9.3). y = 5 at the given point (3, 5), where x = 3. y = 7 near x = 4 (and also near x = 7.7).

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RESPONSE --> ok

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12:14:09 `q006. Suppose the graph you used in the preceding two exercises represents the profit y on an item, with profit given in cents, when the selling price is x, with selling price in dollars. According to your graph what would be the profit if the item is sold for 4 dollars? What selling price would result in a profit of 7 cents? Why is this graph not a realistic model of profit vs. selling price?

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RESPONSE --> the profit would not be as high in the 7 cents as it would be in the 4 dollars but however the graph id not a realistic model for this bc it shows a downward curve

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12:14:21 To find the profit for a selling price of x = 4 dollars, we would look at the x = 4 point on the graph. This point is easily located by sketching a vertical line through x = 4. Projecting over to the y-axis from this point, you should have obtained an x value somewhere around 7. The profit is the y value, so to obtain the selling price x corresponding to a profit of y = 7 we sketch the horizontal line at y = 7, which as in a preceding exercise will give us x values of about 4 (or x = 7.7, approx.).

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RESPONSE --> ok

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12:15:47 `q007. On another set of coordinate axes, plot the points (-3, 4) and (5, -2). Sketch a straight line through these points. We will obtain an approximate equation for this line: First substitute the x and y coordinates of the first point into the form y = m x + b. What equation do you obtain?

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RESPONSE --> you get 4= m(-3) = b

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12:15:59 Substituting x = -3 and y = 4 into the form y = m x + b, we obtain the equation 4 = -3 m + b. Reversing the sides we have -3 m + b = 4.

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RESPONSE --> ok

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12:16:21 `q008. Substitute the coordinates of the point (5, -2) into the form y = m x + b. What equation do you get?

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RESPONSE --> you get -2 = m * 5 +b

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12:16:30 Substituting x = 5 and y = -2 into the form y = m x + b, we obtain the equation -2 = 5 m + b. Reversing the sides we have 5 m + b = -2

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RESPONSE --> ok

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12:16:37 `q009. You have obtained the equations -3 m + b = 4 and 5 m + b = -2

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RESPONSE --> yes

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12:20:18 . Use the method of elimination to solve these simultaneous equations for m and b.

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RESPONSE --> 4 = -3 m + b -2 = 5 m + b 2*4 = -3*2m + 2b -2*-2 = -2*5m -2b 8 = -6m + 2b 4 = -10m -2b 8 = -6m 4 = -10m

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12:20:59 Starting with the system -3 m + b = 4 5 m + b = -2 we can easily eliminate b by subtracting the equations. If we subtract the first equation from the second we obtain -8 m = 6, with solution m = -3/4. Substituting this value into the first equation we obtain (-3/4) * -3 + b = 4, which we easily solve to obtain b = 7/4. To check our solution we substitute m = -3/4 and b = 7/4 into the second equation, obtaining 5 ( -3/4) + 7/4 = -2, which gives us -8/4 = -2 or -2 = -2.

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RESPONSE --> ok I did not understand what process to use

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12:21:53 `q010. Substitute your solutions b = 7/4 and m = -3/4 into the original form y = m x + b. What equation do you obtain? What is the significance of this equation?

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RESPONSE --> y = -3/4x + 7/4 the equation is significant because it is the equation for slope

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12:22:04 Substituting b = 7/4 and m = -3/4 into the form y = m x + b, we obtain the equation y = -3/4 x + 7/4. This is the equation of the straight line through the given points (-3, 4) and (5, -2).

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RESPONSE --> ok

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