Write three equations such that they form a system of equations with y = 5x - 3. the systems should have no, one, and infinitely many solutions, respectively.

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Mathematics

Clark Blevins

5 February, 05:37

Write three equations such that they form a system of equations with y = 5x - 3. the systems should have no, one, and infinitely many solutions, respectively.

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Alfonso Michael · Answer 1

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i. e. the two equations are the same or a multiple of each other.

Example of an equation that will form a system of equations with y = 5x - 3 such that the system will have infinitely many solutions is 2y - 10x = - 6

For a system of linear equations to have no solution, the lines representing the equations must be parallel but not coincide, i. e. they must have the same slope.

Example of an equation that will form a system of equations with y = 5x - 3 such that the system will have no solution is 2y = 10x

Otherwise, the system will have one solution.

Example of an equation that will form a system of equations with y = 5x - 3 such that the system will have one solution is 6y = 2x - 6