Single correct · +4 / −1

Using Cramer's rule, the solution to x + y = 5, x - y = 1 is:

  1. (a) x=3, y=2
  2. (b) x=2, y=3
  3. (c) x=4, y=1
  4. (d) x=5, y=0
Answer and solution

Answer (a) x=3, y=2

Solution

Maths sir · 3 steps

Find three 2 by 2 determinants, then divide: x is Dx over D, y is Dy over D.

  1. Main determinant. Write the coefficients of x and y as a determinant. D = |1, 1; 1, -1| = (1)(-1) - (1)(1) = -2. Since D ≠ 0, there is exactly one solution.
  2. Replace one column. For Dₓ, put the constants 5, 1 in the x column: Dₓ = |5, 1; 1, -1| = -5 - 1 = -6. For D_y, put them in the y column: D_y = |1, 5; 1, 1| = 1 - 5 = -4.

    x = Dₓ/D = -6/-2 = 3, y = D_y/D = -4/-2 = 2

  3. So. The solution is x = 3, y = 2. Check: 3 + 2 = 5 and 3 - 2 = 1. The answer is (a).

The idea to keep. In Cramer's rule, the constants replace the column of the variable you want. Always check D ≠ 0 first, and put your answer back into both equations.

Answer from the NTA final answer key. Solution by PrepWiser.

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