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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5x − 6y = 3 10x − 12y = 6 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =

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ANSWER

Infinitely many solutions.

EXPLANATION

The given system of equations is

[tex]5x - 6y = 3...(1)[/tex]

[tex]10x - 12y = 6....(2)[/tex]

Divide equation (2) by 2.

[tex]5x - 6y = 3...(3)[/tex]

We can see that equation (3) is the same as equation (1).

The two equations will coincide when graphed.

The have the same slope and y-intercept.

This implies that, the system of equations has infinitely many solutions.

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