Question

The sum of the digit of a two-digit number is 12. if the new number formed by reversing the digit is greater than the original number by 54, find the original number. check your solution
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Answer 1

Answer:

39

Step-by-step explanation:

x + 10y = z ..... (1)

x + y = 12 ..... (2)

y + 10x = z + 54 ..... (3)

x + 10y - z = 0

x + y + 0z = 12

10x + y - z = 54

Δ = $\left[\begin{array}{ccc}1&10&-1\\1&1&0\\10&1&-1\end{array}\right]$ = 18

$A_{x}$ = $\left[\begin{array}{ccc}0&10&-1\\12&1&0\\54&1&-1\end{array}\right]$ = 162

$A_{y}$ = $\left[\begin{array}{ccc}1&0&-1\\1&12&0\\10&54&-1\end{array}\right]$ = 54

$A_{z}$ = $\left[\begin{array}{ccc}1&10&0\\1&1&12\\10&1&54\end{array}\right]$ = 702

x = $\frac{A_{x} }{A}$ = 9

y = $\frac{A_{y} }{A}$ = 3

z = $\frac{A_{z} }{A}$ = 39 is the original number

Check the solution: 39 + 54 = 93

Answer 2

Answer:

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