Which of these systems of linear equations has an infinite number of solutions?
3 x minus 8 y = 21. 6 x minus 16 y = 46.
3 x + 6 y = 22. 6 x + 12 y = 44.
5 x + 7 y = 24. 10 x minus 14 y = 48.
5 x minus 9 y = 20. 10 x + 18 y = 40.

3 x + 6 y = 22. 6 x + 12 y = 44.

Step-by-step explanation:

A system of linear equations ha an infinite number of solutions if the two equations, including the right side of the equality, are multipled of each other.

If the left side of both equations are multiples, while the left side is not, the equation has no solutions.

a)

3x - 8y = 21

6x - 16y = 46

Left side multiple, since 6x - 16y = 2(3x - 8y), but 46 is not 2*21. So it has no solutions.

b)

3x + 6y = 22

6x + 12y = 44

Both equations are multiple of each other, in their entirity. So this system has an infinite number of solutions.

c)

5x + 7y = 24

10x - 14y = 48

5x + 7y and 10x - 14y are not multiples. So this system does not have an infinite number of solutions.

3x + 6y = 22

6x + 12y = 44

d)

5x - 9y = 20

10x + 18y = 40

5x - 9y and 10x + 18y are not multiples. So this system does not have an infinite number of solutions.

This means that the answer is:

3 x + 6 y = 22. 6 x + 12 y = 44.

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step-by-step explanation:

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step-by-step explanation:

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