NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.4

Question 5

We need to find the points where these three lines meet each other. Each pair of lines will intersect at one vertex of the triangle.

Step 1: Intersection of Line 1 (\(3x - y = 3\)) and Line 2 (\(2x - 3y = 2\))

From Line 1: \(3x - y = 3 \Rightarrow y = 3x - 3\).

Now substitute this value of \(y\) into Line 2:

\(2x - 3(3x - 3) = 2\)

\(2x - 9x + 9 = 2\)

\(-7x + 9 = 2\)

\(-7x = -7\)

\(x = 1\).

When \(x = 1\), \(y = 3(1) - 3 = 0\).

So, first vertex = (1, 0).

Step 2: Intersection of Line 2 (\(2x - 3y = 2\)) and Line 3 (\(x + 2y = 8\))

From Line 3: \(x + 2y = 8 \Rightarrow x = 8 - 2y\).

Now substitute this into Line 2:

\(2(8 - 2y) - 3y = 2\)

\(16 - 4y - 3y = 2\)

\(16 - 7y = 2\)

\(-7y = -14\)

\(y = 2\).

If \(y = 2\), then \(x = 8 - 2(2) = 4\).

So, second vertex = (4, 2).

Step 3: Intersection of Line 3 (\(x + 2y = 8\)) and Line 1 (\(3x - y = 3\))

From Line 3: \(x = 8 - 2y\).

Substitute this into Line 1:

\(3(8 - 2y) - y = 3\)

\(24 - 6y - y = 3\)

\(24 - 7y = 3\)

\(-7y = -21\)

\(y = 3\).

If \(y = 3\), then \(x = 8 - 2(3) = 2\).

So, third vertex = (2, 3).

Final Answer:

The triangle formed has vertices at \((1,0)\), \((4,2)\), and \((2,3)\).