Let 'x' be the tens digit
'y' be the ones digit
'x(10) + y' is the two-digit number
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-the units digit is one more than 4 times the tens
y = 4x + 1 ------equation 1
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-the sum of the digits is 11
x + y = 11 ----equation 2
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substitute equation 1 to equation 2
x + y = 11
x + 4x + 1 = 11
Transpose 1 to the right side of the equation
x + 4x = 11 - 1
5x = 10
x = 2
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substitute x=2 to equation 1
y = 4x + 1
y = 4(2) + 1
y = 8 + 1
y = 9
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the number as stated above in the variable designation is 10x + y
10x + y = 10(2) + 9
= 20 + 9
= 29
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Therefore the two-digit number is 29.
