Answer :
Let's solve the given system of linear equations step by step:
[tex]\[ \begin{array}{l} x + 2y = 5 \\ 2x + y = 16 \end{array} \][/tex]
Step 1: Solve the first equation for [tex]\( x \)[/tex]:
[tex]\[ x + 2y = 5 \implies x = 5 - 2y \][/tex]
Step 2: Substitute [tex]\( x = 5 - 2y \)[/tex] into the second equation:
[tex]\[ 2(5 - 2y) + y = 16 \][/tex]
Step 3: Simplify the substituted equation:
[tex]\[ 10 - 4y + y = 16 \implies 10 - 3y = 16 \][/tex]
Step 4: Solve for [tex]\( y \)[/tex]:
[tex]\[ -3y = 16 - 10 \implies -3y = 6 \implies y = -2 \][/tex]
Step 5: Substitute [tex]\( y = -2 \)[/tex] back into the expression for [tex]\( x \)[/tex]:
[tex]\[ x = 5 - 2(-2) = 5 + 4 = 9 \][/tex]
Step 6: Compute [tex]\( x + y \)[/tex]:
[tex]\[ x + y = 9 + (-2) = 7 \][/tex]
Thus, [tex]\( x + y \)[/tex] equals 7, so the correct answer is:
[tex]\[ \boxed{\mathbf{7}} \][/tex]
[tex]\[ \begin{array}{l} x + 2y = 5 \\ 2x + y = 16 \end{array} \][/tex]
Step 1: Solve the first equation for [tex]\( x \)[/tex]:
[tex]\[ x + 2y = 5 \implies x = 5 - 2y \][/tex]
Step 2: Substitute [tex]\( x = 5 - 2y \)[/tex] into the second equation:
[tex]\[ 2(5 - 2y) + y = 16 \][/tex]
Step 3: Simplify the substituted equation:
[tex]\[ 10 - 4y + y = 16 \implies 10 - 3y = 16 \][/tex]
Step 4: Solve for [tex]\( y \)[/tex]:
[tex]\[ -3y = 16 - 10 \implies -3y = 6 \implies y = -2 \][/tex]
Step 5: Substitute [tex]\( y = -2 \)[/tex] back into the expression for [tex]\( x \)[/tex]:
[tex]\[ x = 5 - 2(-2) = 5 + 4 = 9 \][/tex]
Step 6: Compute [tex]\( x + y \)[/tex]:
[tex]\[ x + y = 9 + (-2) = 7 \][/tex]
Thus, [tex]\( x + y \)[/tex] equals 7, so the correct answer is:
[tex]\[ \boxed{\mathbf{7}} \][/tex]
