Q: What is a linear expression?

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No, if there is a sqaured variable, the equation is not linear.

It is a linear expression.

It is a linear expression in two variables. As an expression it cannot be solved. Furthermore, to solve equations in two variables you need at least two linear equations.

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It could be a function or a linear expression.

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No, if there is a sqaured variable, the equation is not linear.

It isa linear expression,a binomial expression,an algebraic expression,a polynomial expression.

No, it could be a constant.

I think the word you're looking for is "exponential". A linear expression is of the form ax + b whereas an exponential expression is of the form x^a + b.

It is a linear expression.

It is a linear expression in two variables.

It is a linear expression.

It is a linear expression in two variables. As an expression it cannot be solved. Furthermore, to solve equations in two variables you need at least two linear equations.

Without an equality sign the given expression can't be considered to be a linear equation.

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No, it is simply an expression, not an equation of any kind.