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

1 Answer
Jun 24, 2018

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".