NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.3

Question 8

In a rectangle, opposite sides are equal in length.

So we can write two equations:

Top = Bottom → \(x + 3y = 13\)

Left = Right → \(3x + y = 7\)

Step 1: Start with the second equation.

\(3x + y = 7\)

Subtract \(3x\) from both sides:

\(y = 7 - 3x\)

Step 2: Put this value of \(y\) into the first equation.

The first equation is:

\(x + 3y = 13\)

Replace \(y\) with \(7 - 3x\):

\(x + 3(7 - 3x) = 13\)

Step 3: Expand the brackets:

\(x + 21 - 9x = 13\)

Step 4: Combine like terms:

\(-8x + 21 = 13\)

Step 5: Subtract 21 from both sides:

\(-8x = -8\)

Step 6: Divide both sides by \(-8\):

\(x = 1\)

Step 7: Now find \(y\) using \(y = 7 - 3x\):

\(y = 7 - 3(1)\)

\(y = 7 - 3 = 4\)

So the solution is:

\(x = 1\) and \(y = 4\).