Find the Values of x and y

Video Explanation

Question

In a rectangle, the lengths of the sides are:

\[ 13,\; 7,\; (x + 3y),\; (3x + y) \]

Find the values of \(x\) and \(y\).

Solution

Step 1: Use the Property of a Rectangle

Opposite sides of a rectangle are equal.

Hence,

\[ x + 3y = 13 \quad (1) \]

\[ 3x + y = 7 \quad (2) \]

Step 2: Express One Variable in Terms of the Other

From equation (2):

\[ y = 7 – 3x \quad (3) \]

Step 3: Substitute in Equation (1)

Substitute equation (3) into equation (1):

\[ x + 3(7 – 3x) = 13 \]

\[ x + 21 – 9x = 13 \]

\[ -8x = -8 \]

\[ x = 1 \]

Step 4: Find the Value of y

Substitute \(x = 1\) into equation (3):

\[ y = 7 – 3(1) = 4 \]

Conclusion

The required values are:

\[ x = 1,\quad y = 4 \]

\[ \therefore \quad \text{The values of } x \text{ and } y \text{ are } 1 \text{ and } 4. \]