Write two linear expression with a sum of -5 + 4

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

Algebra

1 Answer

Alan N.

Jun 24, 2018

Sometimes

Explanation:

Consider the two linear expressions with real coefficients

{

a

,

b

}

≠

0

below.

a

1

x

+

b

1

y

a

2

x

+

b

2

y

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".

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