Question

Solve for x and y: `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O

Answer 1

Given that: x = `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O

L.H.S. `x[(2),(1)] + y[(3),(5)] + [(-8),(-11)]` = O

⇒ `[(2x),(x)] + [(3y),(5y)] + [(-8),(-11)]` = O

⇒ `[(2x + 3y - 8),(x + 5y - 11)] =[(0),(0)]`

Comparing the corresponding elements of both sides, we get,

2x + 3y – 8 = 0

⇒ 2x + 3y = 8   .....(1)

x + 5y – 11 = 0

⇒ x + 5y = 11  ......(2)

Multiplying equation (1) by 1 and equation (2) by 2, and then on subtracting, we get,

2x +   3y =    8
2x + 10y =   22
(–)     (–)       (–)  
        –7y  = –14

∴ y = 2

Putting y = 2 in equation (2) we get,

x + 5 × 2 = 11

⇒ x + 10 = 11

x = 11 – 10 = 1

Hence, the values of x and y are 1 and 2 respectively.