Iftwo-thirdofa number increased by 10isequal to14,find the number
1 answer:
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Answer:
C: (2,3)
Step-by-step explanation:
to solve this algebraically just plug in the x and y values of the points and see if they are true, but here is the graph to juse show you
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