First, put the number that the variable is equal to on the left, then put the leading coefficient inside and every coefficient after that on the left. If there's a term missing, for example this is missing an x2, put a zero in the spot it would be in. Then, take the leading coefficient down to the bottom. [Then multiply it by the number on the left and place it under the place where the next coefficient is. Then add those numbers and put the sum below them.] Repeat the steps that are surrounded by brackets until you get the answer, which is the number that is on the lower right.
Example:
For 4x4+6x3-3x-4 when x=2
2|4 6 0 -3 -4
Bring 4 down. Multiply by 2 to get 8. Add 6 to get 14. Multiply by 2 to get 28. Add 0 to get 28. Multiply by 2 to get 56. Add -3 to get 53. Multiply by 2 to get 106. Add -4 to get 102. 102 is the answer.
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The reason is because when you multiply by the number 1 you're not changing the other number at all, so using synthetic substitution with 1 just gets you adding the first to coefficients first, then the sum of that and the next one, and so on.
There is not Substitution Property of Congruence. There is, however, one for Equality, called the Substitution Property of Equality.
You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.
In mathematics substitution is when one term in an equation is replaced by another that has a known value. This is so that the equation itself can be resolved.
By elimination or substitution