Respuesta :

Answer:

  (x, y) = (9, 17)

Step-by-step explanation:

Any two pairs of equations can be used to form a system of equations that will give appropriate values of x and y. Let's set the upper and lower left expressions equal to the middle one.

  2x +3y -20 = 4x +5y -72 . . . . upper left = middle

  52 = 2x +2y . . . . . . . . add 72-2x-3y

  x + y = 26 . . . . . . . . . . divide by 2

and ...

  5x -2y +38 = 4x +5y -72 . . . . lower left = middle

  110 = -x +7y . . . . . . . . . . . . . add 72-5x+2y

Now we have two equations in two unknowns that will give us the common values of x and y. Adding these equations eliminates x and gives the value of y:

  (x +y) +(-x +7y) = (26) +(110)

  8y = 136 . . . . . . . . simplify

  y = 17 . . . . . . . . . divide by 8

  x = 26 -y = 26 -17 = 9

The values of x and y that make all of these expressions equal are ...

  (x, y) = (9, 17)

The value they are equal to is ...

  2x +3y -20 = 2(9) +3(17) -20 = 18 +51 -20 = 49

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Check

  upper right = 9 -4(17) +108 = 9 -68 +108 = 49

  lower right = 3(9) -17 +39 = 27 -17 +39 = 49

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