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(5)Find the values of kfor which the system of equations ˆ x+ ky= 1 kx+ y= 1 has (a)no solution. Answer: . (b)exactly one solution. Answer: . (c)in nitely many solutions. Answer: . (d)When there is exactly one solution, it is x= and y= . (6)Consider the following two systems of equations. 8 >< >: x+ y+ z= 6 x+ 2y+ 2z= 11 2x+ 3y 4z= 3 (1) and 8 ...

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  • Linear equations with no solution or all real numbers Show Step-by-step Solutions Try the free Mathway calculator and problem solver below to practice various math topics.
  • Dec 18, 2013 · Solve the following systems of equations using any method. Solve the following systems of equations. State if they have 1 solution, no solutions, or an infinite number of solutions. Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of ...

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The two equations intersect at exactly one point, so they are consistent and independent. Graph each system and determine the number of solutions that it has. If it has one solution, name it. y = í3 y = x í 3 62/87,21 The graphs intersect at one point, so there is one solution. The lines intersect at (0, ±3). y = 4x + 2 y = í2x í 62/87,21

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  • In this case, equation \(\eqref{eq:linear-equation-in-y-and-k}\) can never hold, as it leads to the contradictory statement that \(9 = 0\). There are therefore no solutions. Approach 2: Using coordinate geometry. Each of the two equations can be considered as the equation of a straight line. In general, these two lines will meet in one point.
  • 3. Without graphing, you can tell a system of equations has infinite solutions because their slopes and y-intercepts are _____. That means they share/have _____ point(s) in common. Graph each line to determine if the following systems of equations have a single solution, no solutions, or infinite

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a) For some vector b the equation Ax= b has exactly one solution. b) For some vector b the equation Ax= b has infinitely many solutions. c) For some vector b the equation Ax= b has no solution. d) For all vectors b the equation Ax= b has at least one solution. 20. Let A : Rn → Rk be a real matrix, not necessarily square.

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One Solution, No Solution, or Infinitely Many Solutions - Consistent & Inconsistent Systems. This algebra video tutorial explains how to determine if a system of equations contain one solution, no solution, or infinitely many ...

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Improve your math knowledge with free questions in "Find the number of solutions" and thousands of other math skills.

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A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.

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Solving Equations with Infinite Solutions or No Solutions ... solution in other types of equations that are not linear, but it is also possible to have no solutions or infinite solutions. No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable.

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As shown in the examples posted by others, linear dependence occurs when one equation in the system of equations can be shown to be a multiple of another. This is ultimately what Gaussian elimination or computing the determinant reveals. In this instance, there is no unique solution to the system of equations.

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