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Questions and Answers
What is required for a meaningful linear equation with n variables?
What is required for a meaningful linear equation with n variables?
- At least one coefficient is zero
- Not all coefficients are zero (correct)
- All coefficients are zero
- At least one variable is zero
What is the general form of a linear equation with n variables?
What is the general form of a linear equation with n variables?
- $a_{1}x_{1}+a_{n}x_{n}+b=0$
- $a_{1}x_{1}+a_{2}x_{2}+...+a_{n}x_{n}=0$
- $a_{1}x_{1}+ ext{...}+a_{n}x_{n}+b=0$ (correct)
- $a_{1}x_{1}+a_{2}x_{2}+...+a_{n}x_{n}=b$
How many solutions does a linear equation with just one variable have?
How many solutions does a linear equation with just one variable have?
- Infinitely many solutions
- No solution
- Exactly two solutions
- Exactly one solution (if $a_{1} \neq 0$) (correct)
What can be interpreted as the solutions of a linear equation in two variables?
What can be interpreted as the solutions of a linear equation in two variables?
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What geometric shape do the solutions of a linear equation form in the Euclidean plane?
What geometric shape do the solutions of a linear equation form in the Euclidean plane?
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