Question

Find the sum of the following expression: $3a + b;5a + 2b;3a - b$

Answer 1

Hint: According to the question we find the sum of $3a + b;5a + 2b;3a - b$ So, in the question there are three linear equations with two variables a and b. We know that if a variable is given in x that it can be added and subtracted with the same variable x to obtain the result.
As we know that when a negative number/term or variable is added with the negative number/term or variable then the result will be the addition of both of the number/term or variable but the sign will be negative but if a negative number/term or variable is added with the positive number/term or variable then the result will be the subtraction of both of the number/term or variable but the sign will be depend on the greater number.
Hence, first of all we will add the terms $3a + b$ and $5a + 2b$ the term with variable a will be added with the term having variable a and same as term with variable b will be added with the term having variable b and after that we will add the obtained expression after addition with the remaining term $3a - b$.

Complete step-by-step answer:
Step 1: First we have to add the terms $3a + b$ and $5a + 2b$ the term with variable a will be added with the term having variable a and same as term with variable b will be added with the term having variable b.
$
   = (3a + b) + (5a + 2b) \\
   = 3a + b + 5a + 2b \\
   = 8a + 3b
 $
Step 2: Now, we have to add the obtained addition of the terms $3a + b$ and $5a + 2b$ obtained $8a + 3b$ as in step 1 with the remaining term $3a - b$.
$
   = (8a + 3b) + (3a - b) \\
   = 8a + 3a + 3b - b \\
   = 11a + 2b
 $

Hence, the sum of the following expression: $3a + b;5a + 2b;3a - b$ is $ = 11a + 2b$

Note: A negative term is added with the negative term then the result will be the addition of both of the terms but the sign will be negative but if a negative term is added with the positive term then the result will be the subtraction of both of the terms but the sign will be dependent on the greater number.