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Which equation has exactly one solution in common with the equation y = 6x - 2?

18x-3y=6
(1/2)y=3x-2
2y=4x-12
18x-12-3y

User Hildy
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The answer to which equation has exactly one solution in common with the equation y = 6x - 2 is D, 18x-12-3y
User David Hicks
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Answer: 18x-12-3y

Explanation:

To find which equation has exactly one solution in common with y = 6x - 2, we need to determine the point where they intersect.

Substituting y = 6x - 2 into the equations given, we get:

18x - 3(6x - 2) = 6

Simplifying this equation gives us:

x = 2

Substituting x = 2 into y = 6x - 2, we get:

y = 6(2) - 2 = 10

Therefore, the point where y = 6x - 2 intersects with the other equations is (2, 10).

Now, we can substitute x = 2 and y = 10 into each of the other equations to see which ones have exactly one solution:

(1) 18x - 3y = 6:

18(2) - 3(10) = 6

36 - 30 = 6

This equation does not have exactly one solution at (2, 10).

(2) (1/2)y = 3x - 2:

(1/2)(10) = 3(2) - 2

5 = 4

This equation does not have exactly one solution at (2, 10).

(3) 2y = 4x - 12:

2(10) = 4(2) - 12

20 = 0

This equation does not have exactly one solution at (2, 10).

(4) 18x - 12 - 3y = 0:

18(2) - 12 - 3(10) = 0

36 - 12 - 30 = 0

This equation has exactly one solution at (2, 10).

Therefore, the equation that has exactly one solution in common with y = 6x - 2 is 18x - 12 - 3y = 0.

User UnknownOctopus
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