Question

if 11 X + 3 Y is equal to 28 and 3 X + 11 Y is equal to 14, then X + Y is equal to​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{11x+3y=28}\,\,\,\,...(1)\\ \tt{3x+11y=14\,\,\,\,...(2)}$

Add (1) and (2),

$\sf{14x+14y=42}$

$\sf{\implies14(x+y)=42}$

$\sf{\implies(x+y)=3}$

Answer 2

According to the question

$\large\bf{\red{ \longrightarrow}}\rm \: 11x \: + \: 3y \: = \: 28 \: \quad \large\bf{\blue{ \: . \: . \: . \small ( equation \: 1)}}$

$\large\bf{\red{ \longrightarrow}}\rm \: \: 3x \: + \: 11y \: = \: 14 \quad \large\bf{\blue{ \: . \: . \: . \small ( equation\:</u></strong><strong><u>2</u></strong><strong><u>)}}$

Now , Adding equation 1 and equation 2

$\begin{cases} \ \bf{\purple{ \implies}} \rm \: 11x \: + \: 3y \: = \: 28 \: + \: 3x \: + \: 11y \: = \: 14 \\ \\ \rm{\orange{ Combining \: \: like \: \: terms}} \\ \\ \bf{\purple{ \implies}} \rm \: 11x \: + \: 3x \: + 11y \: + \: 3y \: = \: 28 \: + \: 14 \\ \\ \bf{\purple{ \implies}} \rm \: 14x \: + \: 14y \: = \: 42 \\ \\ \bf{\purple{ \implies}} \rm \:14 \: (x + y) \: = \: 42 \\ \\ \bf{\purple{ \implies}} \rm \:(x + y) \: = \: \cancel\frac{{42} }{14} \\ \\ \bf{\purple{ \implies}} \rm \:(x + y) \: = \: 3\end{cases}$