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.