[最も選択された] 3x-y=2 2x-y=3 graphical method 653337
Ex 6 3 2 Solve 3x 2y 12 X 1 Y 2 Graphically
Graph of 2x y 1 = 0 and 2x y = 9 on the same axes Use 2 cm = 1 unit on both axes and plot only 3 points per line Write down the coordinates of the point of intersection of the two linesThe coordinates of the point of intersection would be the solution to the system of equations If the two graphs do not intersect which means that they are parallel then there is no solution Example Using the graphical method, find the solution of the systems of equations y x = 3
3x-y=2 2x-y=3 graphical method
3x-y=2 2x-y=3 graphical method-Solving Systems Graphical Method Step 1 Graph both equations Step 2 Find the point of intersection y x x 2y = 7 x – y = 4 x y x y 0 3 ½ 0 4 1 3 1 3 Solution (5, 1) Solving Systems Substitution Method y x x 2y = 7 x y = 4 Step 1 Solve for x or y in 1 equation Step 2 Substitute into the 2nd equation Step 3 Solve algebraicallyY = 5 x y = 5 – 3 Therefore, we get the value of y = 2 Hence, the value of x = 3 and the value of y = 2 Question 2) Solve for the values of 'x' and 'y' 2x 6y = 10 1x – 2y = 15
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2 Pick a test point, (a,b), lying in one of the halfplanes determined by the line sketched in Step 1 and substitute the numbers a and b for the values of x and y in the given inequality For simplicity, use the origin, (0,0), whenever possible 3 If the inequality is satisfied (True), the graph of the solution to the inequality is the halfplaneThe Graphical Simplex Method An Example Consider the following linear program Max 4x1 3x2 Subject to 2x1 3x2 6 (1) 3x1 2x2 3 (2) 2x2 5 (3) 2x1 x2 4 (4) x1;4y = 3x24 4y < 3x24 4y > 3x24 y = 3 4 x6 y > 3 4 x6 y < 3 4 x6 Thethreesolutionsetsabove aredisjoint (donotintersector overlap), andtheir graphs fill up the plane We are familiar with the graph of the linear equation The graph of one inequality is all the points on one side of the line, the graph of the other all the points on the other
Solve using the Graphical method the following problem Maximize Z = f (x,y) = 3x 2y subject to 2x y ≤ 18 2x 3y ≤ 42 3x y ≤ 24 x ≥ 0 , y ≥ 0 Initially the coordinate system is drawn and each variable is associated to an axis (generally 'x' is associated to the horizontal axis and 'y' to the vertical one), as shown inHence, the maximum value of Z is 18 at the point (4, 3) 6 Minimise Z = x 2y subject to Solution The feasible region determined by the constraints, 2x y ≥ 3, x 2y ≥ 6, x ≥ 0, and y ≥ 0, is given below A (6, 0) and B (0, 3) are the corner points of the feasible region The values of Z at the corner points are given belowRewrite the equation as − 3 2 x 2 = 0 3 2 x 2 = 0 − 3 2 x 2 = 0 3 2 x 2 = 0 Add 3 2 3 2 to both sides of the equation x 2 = 3 2 x 2 = 3 2 Since the expression on each side of the equation has the same denominator, the numerators must be equal x = 3 x = 3 Multiply both sides of the equation by 2 2
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Y ≥ 0 2) _____ A) Maximum of 1 when x = 3 and y = 8 B) Maximum of 100 when x = 8 and y = 3 C) Maximum of 92 when x = 4 and y = 5 D) Maximum of 96 when x = 9 and y = 2 A manufacturer of wooden chairs and tables must decide in advance how 3x – y = 2;
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