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at(3,1)= -2 2. Consider the following system of equations: 2x - y20 2y - 3x s...
1. Solve the following system of equations using Gauss-Jordan elimination. 3x - 2y +4z=3 2x +2y-2z=4 x+4y- &z=1
5. Consider the system of equations: 2 - Y + 2z = 4 3x - 2y + 92 = 14 2. - 4y + az = b. Find all the values of a and b so that the system has a) no solution b) 1 solution e) exactly 3 solutions and 4) infinitely many solutions.
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint 3: x-3y 2-2 2x-y-1 4 x +2y 8 4 7 a. (3 points) Shade the feasible region in the graph provided above. b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) in the above graph Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s).
Systems of Equations: 3x + y = 6 2x-2y=4 Substitution: Elimination: Solve 1 equation for 1 variable. Find opposite coefficients for 1 variable. Rearrange. Multiply equation(s) by constant(s). Plug into 2nd equation Add equations together (lose 1 variable). Solve for the other variable. Solve for variable. Then plug answer back into an original equation to solve for the 2nd variable. y = 6 -- 3x solve 1" equation for y 6x +2y = 12 multiply 1" equation by 2 2x...
(1 point) Given the system of inequalities below, determine the shape of the feasible region and find the vertices of the feasible region. x + y = 6 2x + y 2 10 x + 2y 27 x 20 y20 The shape of the feasible region: Quadrilateral List the vertices (as a list of points such as "(2,3), (5,7), (0,0)"):
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w....
Solve the following linear equations by graphical method. 2x - y = 1 3x + 2y = 4
Locate the solution region
Find the corners. (Select all that apply.)
(0, 5/2)
(0, 2)
(0, 5)
(0, 6)
(1, 2)
(1, 3)
(5/3, 0)
(2,1)
(3,1)
(5,0)
(6,0)
The graph of the boundary equations for the system of inequalities is shown with the system. 2x + 6y 2 12 3x + 6y > 15 6x + 2y > 10 x20, y20 6x + 2y = 10 3x + y = 15 2x + y = 12
Question 12 (4 points) Solve the System of Equations 2x - 5y = 13 3x + 4y = –15 O (-1,-3) 0 (-3,1) (3,1) (1,3) Question 13 (4 points) Solve the System of Equations 7x + 9y = -34 - 4x - 64 = 20 Question 14 (4 points) If f(x) = (3)" then what is f(-3)? O =27 0 0 0 Question 15 (4 points) A bottle of 140 super-vitamins costs $20. If the cost varies directly with the...
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or by any convenient method #13 a) 3x+4y-1 2x-3y-12 b) -4x+3y--!5 3x-2y-4