# Linear System Skills

Note by sandersbay, updated more than 1 year ago
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### Description

Math Note on Linear System Skills, created by sandersbay on 02/26/2014.

## Resource summary

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Algebra Skills: Slope and y-intercept form: y = mx +b Standard form: ax +by +c = 0 Rules: 1.       X must lead and be positive 2.       No fraction Graphing Strategies using standard forms (the x and y intercepts): ax +by =C Y-intercept is when x is zero X-intercept is when y is zero Find the two intercepts on the graph, join them. 1.       Don’t use this strategy if the intercepts are going to be fractions, because it won’t be accurate, use y=mx+b Writing Equations of Lines (using delta y delta x strategy) 2.       Find slope first 3.       m = ∆y/∆x (by substituting one pair of points) Solving Equations with Rational Coefficients Use scalar Solve Linear System (using the method of substitution 1) y = 3x −4 (expression for y),  Substitute into x +y = 8 x+3x-4=8Solve Linear System (using the method of substitution 2)y1 = ax+by2 = cx+dy1=y2ax+b = cx+dSolve Linear System (using the method of elimination)ax+y=cdx+y=e (subtraction)gx+y =o (y is eliminated to get x)Tip: addition is always better than subtraction) Real Life Word problemsA vending machine contains a total of 395  quarters and dimes. The total value of the coins  is \$66.80. How many of each coin are required  to make this amount?q + d = 395  0.25q + 0.10d = 66.80A chemistry student was asked to make 25mL of 48%  alcohol by volume by mixing 40% alcohol solution by  volume and 60% alcohol solution by volume. How many  litres of each alcohol solution must the student use to  make 25mL of 48% alcohol? a40 + a60 = 25  0.40a40 + 0.60a60 = 0.48(25)A store owner sells peanuts of \$4.80/kg and raisins for  \$2.40/kg. She will make a mixture of peanuts and raisins  called Nutsins and sell it for \$3.36/kg. How many  kilograms of peanuts and raisins does she need to make  200kg of Nutsins? r+ p = 200  4.80p + 2.40r = 3.36(200) The length of a rectangle is 19 m longer than its  width. If the perimeter is 606 m, what are the  dimensions of the rectangle? l = w + 19   2l + 2w = 606 When 4 times the larger of two numbers is  added to 3 times the smaller the result is 68.  Seven times the larger number less 5 times the  smaller number is 37. What are the numbers?4l + 3s = 68   7l −5s = 37

Jeanne took a trip from Brownsville to Montreal,  a distance of 830km. She travelled part of the  way by bus and the rest of the way by plane.  The bus averaged 40k/h and the plane averaged  500k/h. The whole trip took 3.5 hours. How  many hours were spent on the bus? p+b = 3.5  500p + 40b = 830 A tailor repairs cuffs on shirts and hems pants.  He can repair 2 cuffs per hour and hem 10 pants  in one hour. In an 8 hour day, how long did he  spend repairing cuffs and how long did he hem  pants if 56 articles of clothing were worked on?c +ℎ = 8   2c +10ℎ = 56  A chocolate chip recipe requires 13kg of butter and  8 kg of oatmeal. A low fat oatmeal cookie recipe  calls for 2kg of butter and 29 kg of oatmeal. You  have 47kg of butter and 140 kg of oatmeal in the  pantry. How many batches of chocolate chip cookies  and how many batches of oatmeal cookies can you  make? 13c + 2a= 47  8c +29a = 140 Geometry property                               ________length of a line: |ab|=/∆y2+∆X2midpoints of a line: (x1+x2 / 2), (y1+y2 / 2)paralell lines: m1=m2perpendicular lines(right angles): m1=-1/m2opposite side equal length? |ab|=|dc|does the two lines bisect?1.find the midpoint2.find the point of intersection (slope first, delta x and delta y)3.see if the two are the sameDistance between a point to a line:always perpendicular, because it has the shortest distance1. get equation for the line, negative reciprocal=slope, delta x and delta y2. solve system using the two equations of the two lines3. find the distance using the point and the point of intersection, |ab|=/∆y2+∆X2

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