2) Find the distance between the two given points: (5,9) and (13,-5). Round to the hundredths place. *
A 18.44 units
B 16.12 units
C 10.77 units
D 15.24 units

9514 1404 393

  (x, y) = (2, 3)

Step-by-step explanation:

"Removal method" is a new one for me. We presume it is another name for the "elimination" or "addition" method.

Multiply the second equation by 5 and add the first.

  (6x -5y) +5(-4x +y) = (-3) +5(-5)

  -14x = -28 . . . . . simplify

  x = 2 . . . . . . . . . divide by -14

  -4(2) +y = -5 . . . substitute for x in the second equation

  y = 3 . . . . . . . . . add 8

The solution is (x, y) = (2, 3).

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Check

We found y using the second equation, so we know the values of x and y work in that one. We only need to check the values in the first equation.

  6(2) -5(3) = -3

  12 -15 = -3 . . . . . true; answer checks OK