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Questions and Answers
In a linear equation, the ______ are often denoted as $x_1, x_2, ..., x_n$ and the coefficients as $b, a_1, ..., a_n$.
In a linear equation, the ______ are often denoted as $x_1, x_2, ..., x_n$ and the coefficients as $b, a_1, ..., a_n$.
variables
A linear equation can be put in the ______ $a_1x_1 + ... + a_nx_n + b = 0$, where $x_1, ..., x_n$ are the variables and $b, a_1, ..., a_n$ are the coefficients.
A linear equation can be put in the ______ $a_1x_1 + ... + a_nx_n + b = 0$, where $x_1, ..., x_n$ are the variables and $b, a_1, ..., a_n$ are the coefficients.
form
To yield a meaningful equation, the coefficients $a_1, ..., a_n$ are required to not all be ______.
To yield a meaningful equation, the coefficients $a_1, ..., a_n$ are required to not all be ______.
zero
The solutions of a linear equation are the values that, when substituted for the unknowns, make the equality ______.
The solutions of a linear equation are the values that, when substituted for the unknowns, make the equality ______.
In the case of just ______ variable, there is exactly ______ solution (provided that $a_1
eq 0$).
In the case of just ______ variable, there is exactly ______ solution (provided that $a_1 eq 0$).
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called '______', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called '______', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for '______'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for '______'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'
Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'
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Study Notes
Linear Equations
- In a linear equation, variables are often denoted as $x_1, x_2, ..., x_n$ and coefficients as $b, a_1, ..., a_n$.
- A linear equation can be put in the form $a_1x_1 + ...+ a_nx_n + b = 0$, where $x_1, ..., x_n$ are the variables and $b, a_1, ..., a_n$ are the coefficients.
- To yield a meaningful equation, the coefficients $a_1, ..., a_n$ are required to not all be zero.
- The solutions of a linear equation are the values that, when substituted for the unknowns, make the equality true.
Single Variable Linear Equations
- In the case of just one variable, there is exactly one solution (provided that $a_1 ≠0$).
Algebra Etymology
- Algebra is a Medieval Latin short hand for the title of the first book explaining algebraic principles.
- The first book on algebra was called 'al-mukhtasar fi hisab al-jabr wa al-muqabala', which is Arabic for 'the compendium on calculation by restoring and balancing'.
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