Question

The pairs of linear equations which have the unique solution x = 2, y = –3 are

• A. x + y = –1 ; 2x – 3y = –5
• B. 2x + 5y = –11 ; 4x + 10y = –22
• C. 2x – y = 1 ; 3x + 2y = 0
• D. x – 4y –14 = 0 ; 5x – y – 13 = 0

Answer 1

Answer: (A), (D)

The correct options are
A

x + y = –1 ; 2x – 3y = –5

D

x – 4y –14 = 0 ; 5x – y – 13 = 0

1.
x + y = –1 ----(i)

2x + 3y = –5-----(ii)

(i) $\times$ 2 $\to$ 2x + 2y = -2 -----(iii)

(ii) - (iii) $\to$ y = -3. Substitute the value of y in (i) we get x = 2.
(2, -3) is a solution for the given pair of equations.

2.
2x + 5y = –11 -----(i)
4x + 20y = –22-----(ii)
(i) $\times$ 2 $\to$ 4x + 10y = -22 ----(iii)
(iii) - (ii) $\to$ y = 0
(2, -3) is not a solution for the given pair of equations.

3.
2x – y = 1 -----(i)
3x + 2y = 0-----(ii)
(i) $\times$ 2 $\to$ 4x - 2y = 2 -- -(iii)
(iii) + (ii) $\to$ $x=\frac{2}{7}$
(2, -3) is a not solution for the given pair of equations..

4.
x – 4y =14 -----(i)
5x – y = 13 -----(ii)
(ii) $\times$ 4 $\to$ 20x - 4y =52-----(iii)
(iii) - (i) $\to$ x = 2. Substitute the value of x in (i) we get y = -3.
(2, -3) is a solution for the given pair of equations.