Answer:
(x, y) = (9, 17)
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