Determine x + y if (begin{pmatrix} 2 & -3 \ -1 & 4 end{pmatrix}) (begin{pmatrix} x \ y end{pmatrix}) = (begin{pmatrix}-1 \ 8 end{pmatrix})
- A.
3 - B.
4 - C.
7 - D.
12
Correct Answer: Option C
Explanation
(begin{pmatrix} 2 & -3 \ -1 & 4 end{pmatrix} begin{pmatrix} x \ y end{pmatrix} = begin{pmatrix} -1 \ 8 end{pmatrix})
(begin{pmatrix} 2x – 3y \ -x + 4y end{pmatrix} = begin{pmatrix} -1 \ 8 end{pmatrix})
(2x – 3y = -1 … (i))
(-x + 4y = 8 … (ii))
From (ii), x = 4y – 8.
(2(4y – 8) – 3y = -1 implies 8y – 16 – 3y = -1)
(5y = -1 + 16 = 15 implies y = 3)
(x = 4(3) – 8 = 12 – 8 = 4)
(therefore x + y = 3 + 4 = 7)