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

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Answer 1 · 2018-06-24T14:47:49

Sometimes

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

$a_{1} x + b_{1} y$ $a_1x+b_1y$

$a_{2} x + b_{2} y$ $a_2x+b_2y$

The sum of these expressions is:

$(a_{1} + a_{2}) x + (b_{1} + b_{2}) y$ $(a_1+a_2)x + (b_1+b_2)y$

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

The $x -$ $x-$ term will exist in all cases where $a_{1} \neq - a_{2}$ $a_1 != -a_2$

Hence, the sum of two linear expressions will have $x -$ $x-$ term where $a_{1} \neq - a_{2}$ $a_1 != -a_2$

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