Pair of Linear Equations in Two Variables — Questions & Answers

Sample questions from Pair of Linear Equations in Two Variables

1. Q1. Solve 5x−y=9 and 2x+y=12. Verify the related simultaneous-equation calculation:

   • A.(3,6)✓
   • B.(6,3)
   • C.(2,1)
   • D.(1,2)
   Solution

   Adding gives 7x=21, so x=3 and y=6.

2. Q2. If x+y=10 and xy=21, the numbers x and y are:

   • A.3 and 7✓
   • B.2 and 8
   • C.1 and 9
   • D.4 and 6
   Solution

   The pair has sum 10 and product 21, so the numbers are 3 and 7.

3. Q3. The solution of 2x + y = 7 and 3x − y = 8 is:

   • A.x = 1, y = 3
   • B.x = 3, y = 1✓
   • C.x = 2, y = 3
   • D.x = 3, y = −1
   Solution

   B is correct. Adding eliminates y and gives 5x = 15, so x = 3, and substituting back gives y = 1. A swaps the values and fails both equations. C comes from adding wrongly and getting 5x = 10. D takes the sign of y from the second equation, where the term is −y, and reports the value with that sign attached.

4. Q4. Two distinct parallel lines have:

   • A.no solution✓
   • B.one solution
   • C.infinitely many solutions
   • D.two solutions
   Solution

   Parallel distinct lines never meet.

5. Q5. Two lines drawn from a pair of linear equations intersect at exactly one point. The pair is:

   • A.Consistent with a unique solution✓
   • B.Inconsistent
   • C.Consistent with infinitely many solutions
   • D.Neither consistent nor inconsistent
   Solution

   A is correct. A pair with at least one solution is consistent, and one crossing point means exactly one solution. B describes a pair with no solution, which is the parallel case. C describes coincident lines, which meet everywhere rather than at one point. D invents a third category that does not exist, since every pair is one or the other.

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