Question

In the matrix equation below, what are the values of x and y?

Answer 1

(d) x = 5, y = 2 are the correct values of the given system.

Explanation:

Here, in the given Matrix expression,

By matrix multiplication with a scalar, we get

`(1)/(2) ( x +3)  - 3(-1) = 7`

and
`(1)/(2)(8)  -3(y +1)  = -5`

Solving the above expression, we get

`(1)/(2) ( x +3) + 3 = 7  \implies (1)/(2) ( x +3) = 4\\or, (x+3) = 2(4)  = 8\\\implies x = 8-3 = 5`

or, x = 5

Solving for y, we get:

`(1)/(2)(8)  -3(1) -3(y +1)  = -5  \implies 4  -3y - 3 = -5\\or, 1 + 5 = 3y\\or, 6 = 3y \implies y =  (6)/(3) = 2\\`

or, y = 2

Hence, x = 5, y = 2 are the correct values of the given system.