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Rearrange and solve the system in the picture: -6 + 5x = 6y and 4y + 14 = 5x.

a) (4, 6)
b) (0, 3)
c) (6, 4)
d) (3, 0)

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Final answer:

The system of linear equations -6 + 5x = 6y and 4y + 14 = 5x are solved to obtain the solution as (x, y) = (6, 4), matching option (c).

Step-by-step explanation:

The problem presented involves solving a system of linear equations. The given system is:

  • -6 + 5x = 6y (1)
  • 4y + 14 = 5x (2)

To solve the system, you can express equation (2) with y on one side to get:

y = (5x - 14)/4 (3)

Replace y in equation (1) with the expression from equation (3) to solve for x:

-6 + 5x = 6((5x - 14)/4)

Multiply both sides by 4 to clear the denominator:

-24 + 20x = 30x - 84

Combine like terms:

-24 + 84 = 30x - 20x

60 = 10x

x = 6

Now, substitute x back into equation (3) to solve for y:

y = (5(6) - 14)/4

y = (30 - 14)/4

y = 16/4

y = 4

The solution to the system of equations is (x, y) = (6, 4), which corresponds to option (c).

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