Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
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one and only one solution
one and only one solution
one and only one solution
infinitely many solutions
Indicate whether the matrix is in row-reduced form.
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Find the pivot element to be used in the next iteration of the simplex method.
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Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.
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Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9
y = ![]() x + ![]()
y = ![]() x – ![]()
y = –![]() x – ![]()
y = –![]() x + ![]()
10 If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?
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Maximize
P= 10x + 12y
subject to
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Write the equation ![]() in the slope-intercept form and then find the slope and y-intercept of the corresponding line.
Find the slope of the line that passes through the given pair of points.
(2, 2) and (8, 5)
Consider the linear programming problem.
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Sketch the feasible set for the linear programming problem.
Solve the system of linear equations using the Gauss-Jordan elimination method.
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Solve the linear system of equations
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Unique solution:
Unique solution:
Infinitely many solutions:
Determine whether the given simplex table is in the final form. If so, find the solution to the associated regular linear programming problem.
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Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.
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Solve the linear programming problem by the simplex method.
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Metro Department Store’s annual sales (in millions of dollars) during 5 years were
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Annual Sales, y
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5.8
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6.1
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7.2
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8.3
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9
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Year, x
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1
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2
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3
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4
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5
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Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
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Solve the linear system of equations
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Unique solution:
Unique solution:
Infinitely many solutions:
Solve the system of linear equations using the Gauss-Jordan elimination method.
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Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.
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Solve the system of linear equations, using the Gauss-Jordan elimination method.
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Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope – 1.
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