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Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
When solving a system of linear equations with two unknowns, which of the following statements is/are true?
I. If the system has no solution, the equations represent the same line.
II. If the system has infinitely many solutions, at least one variable in the general solution will be arbitrary.
III. The solution to the system of equations must satisfy only one of the equations in the system.
- A.
Only II and III are true.
- B.
Only I is true.
- C.
Only II is true.
- D.
Only I and II are true.
- E.
Only III is true.
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- 1. What is the solution to the system of linear equations shown in the graph below? -4 -3 -2 -2 구arrow_forwardSolve the following system of linear equations: x-y = 4 -4x+4y= -16 Which one of the following statements best describes your solution:A. There is no solution.B. There is a unique solution.C. There are 2 solutions.D. There are infinitely many solutions. Statement: D- There are infinitly many solutions Solve for y in terms of xarrow_forward3. Solve each system of equations using the algebraic method of your choice. (Do not solve by graphing!) Show all of your work completely. State the solution set clearly. Write NO SOLUTION (0) or INFINITELY MANY SOLUTIONS if appropriate. If there are infinitely many solutions, use set builder notation to define the ordered pairs in the solution set. a. b. C. -X- 1 3 x- J5x- 1 y = 2 x + 3 4 1 2 y = Y 6 1 vit 5x-6y=-4 -4x+5y=3 2 13 6 = = 4 x y-5 1 + 12 15 60arrow_forward
- Some values of two linear equations are shown in the tables below. What is the solution to the system of equations represented by these tables? Note: If the solution is an ordered pair, do not put spaces between the comma and the second value. If the solution is "no solution" or "infinitely many solutions," enter those words with spaces and spelled correctly.arrow_forwardWhich of the following statement is true? The equation x-p+ tv describe a line through v parallel to p A homogenenous linear system of equations is always consistent The equation Ax=0 gives an explicit description of its solution set If x is a nontrivial solution of Ax=0, then every entry in x is nonzeroarrow_forward
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