Question

Will the sum of two linear expressions, each with an x-term, always, sometimes, or never have an x-term? Why?

Answer 1

Sometimes

Explanation:

Consider the two linear expressions with real coefficients `{a,b} !=0` below.

`a_1x+b_1y`

`a_2x+b_2y`

The sum of these expressions is:

`(a_1+a_2)x + (b_1+b_2)y`

We are asked about the existance of the `x-`term.

The `x-`term will exist in all cases where `a_1 != -a_2`

Hence, the sum of two linear expressions will have `x-`term where `a_1 != -a_2`

Thus, the answer to this question is: "sometimes".