Pls someone help I need this urgently done
1 answer:
Answer:
and
the mistake was in calculating
let's solve first.
Step-by-step explanation:
if , substitute the
in the equation
as
solve the equation in parentheses :
multiply by
it will equal to:
now we want to let all unknown digits alone, so we will take to the other side with a different sign it will be as:
now we will solve it:
at this part, the given equation was wrong in the paper.
we don't want the digit to be negative so we will do it like this:
now that we found we will substitute it to find
:
overall the mistake was in calculating instead of putting
he/she put a different sign in front of the digit like :
so when he/she flipped it became positive and instead of subtracting he/she added it.
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ANSWER
The general solution is , where
is an integer
<u>EXPLANATION</u>
In order to solve the linear congruence;
We need to determine the inverse of (which is a Bézout coefficient for 33).
To do that we must first use the Euclidean Algorithm to verify the existence of the inverse by showing that;
Now, here we go;
The greatest common divisor is the last remainder before the remainder of zero.
Hence, the .
We now express this gcd of 1 as a linear combination of 33 and 280.
We can achieve this by making all the non zero remainders the subject and making a backward substitution.
Equation (2) in equation (1) gives,
The above linear combination tells us that is the inverse of
.
Now we multiply both sides of our congruence relation by .
This implies that;
.
Since this is modulo, the solution is not unique because any integral addition or subtraction of the modulo (280 in this case) produces an equivalent solution.
Therefore the general solution is,
, where
is an integer