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Q: Does this system of equation 5x - y equals 7 have one solution no solution or an infinite number of solutions?

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There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)

It has infinitely many solutions.

[x + y = 6] has an infinite number of solutions.

It's the equation of a straight line. Every point on the line is a solution to the equation. There are an infinite number of them.

Since the highest power of 'x' in the equation is '1', there's one solution.

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There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)

It has infinitely many solutions.

x - 2y = -6 x - 2y = 2 subtract the 2nd equation from the 1st equation 0 = -8 false Therefore, the system of the equations has no solution.

[x + y = 6] has an infinite number of solutions.

This would be like the equation of a line, with infinite solutions.

There are no candidates below, so none of them. There are an infinite number of solutions to the equation, and from here, we can't see which ones are on your list of choices.

This is an equation of a line. There are an infinite number of solutions which are all points on the line. It is a linear equation.

There is no such pair. The solution to equation 1 and equation 2 is x = 1, y = 1. The solution to equation 2 and equation 3 is x = 1, y = 1. And the solution to equation 1 and equation 3 is any point on the line 3x + 2y = 5 - an infinite number of solutions. The fact that the determinant for equations 1 and 3 is zero (or that they are not independent) does not mean that there is no solution. It means that there is no UNIQUE solution. In this particular case, the two equations are equivalent and so have an infinite number of solutions.

16 = 16 is an identity, not an equation. An identity does not have solutions.

The equation has infinitely many solutions.

One solution: x = -4

There is only one solution to that equation. It's . . . . . x = -16

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