One side of Square A is the hypotenuse of the white triangle. The square of this hypo. is 24^2+10^2 = 576 + 100 = 676. Since the square of the hypo is the area of Square A, Square A has the area 676 sq. in.
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The mistake was when she multiplied the 2nd equation by 5, she forgot to also multiply that last number 10 by 5 as well.
correction :
5x + 3y - z = 15
-x + 2y + 3z = 10...multiply by 5
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5x + 3y - z = 15
-5x + 10y + 15z = 50 (result of multiplying by 5)
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13y + 14z = 65
A and C. I have to type more to get this answer through so whatever.