Write a Pair of Linear Equations with Given Unique Solution

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Write a pair of linear equations which has the unique solution x = −1 and y = 3. How many such pairs can you write?

Step 1: Use the Given Solution

The given solution is:

x = −1, y = 3

So, any linear equation satisfied by these values can be used.

Step 2: Write Two Linear Equations

Choose two different equations satisfied by x = −1 and y = 3.

For example:

x + y = 2  …… (1)

2x + y = 1  …… (2)

Step 3: Verify the Solution

Substitute x = −1 and y = 3 in equation (1):

−1 + 3 = 2 ✔

Substitute x = −1 and y = 3 in equation (2):

2(−1) + 3 = 1 ✔

Hence, the pair of equations has the unique solution x = −1, y = 3.

Step 4: Number of Such Pairs

We can write infinitely many linear equations passing through the point (−1, 3).

By choosing any two non-parallel lines through this point, we get a pair of linear equations with the same unique solution.

Final Answer

One such pair of linear equations is:

x + y = 2 2x + y = 1

Number of such pairs = infinitely many.

Conclusion

Thus, infinitely many pairs of linear equations can be written which have the unique solution (−1, 3).