Question

what is the correct answer?

Answer 1

Answer :

• Option (D) : ( - 5 , - 2)

Basic Concept :

☆ Whenever a matrix is given to us, then the corresponding term which means the 1st term will be equal to the 1st row term of the 1st column, which will be given the matrix in the right hand side is equal to the left hand matrix.

Let's Understand with the help of Example :

$\left[ \begin{array}{ccc} \red{1}&2&3 \\ 1&2&2 \\ 1&2&3 \end{array} \right] = \left[ \begin{array}{ccc} \red{6}&2&3 \\ 4&2&5 \\ 1&7&3 \end{array} \right]$

in this matrix you can see in both right and left hand side matrix , in column first in first row and 1st numbers are red it means 1 = 6 . Also this logic is used in this question!

Solution :

$\left[ \begin{array}{cc} \red{ \sf \: x + 3}&1\\ - 3& \green{\sf3y - 4} \\ \end{array} \right] = \left[ \begin{array}{cc} \red{ \sf \: y}&1 \\ - 3& \green{ \sf2x} \end{array} \right]$

See Red Part :

$\rightarrow \sf \: x + 3 = y \\ \boxed{ \sf \: x - y = - 3} - - (1)$

See Green Part :

$\rightarrow \sf3y - 4 = 2x \\ \boxed{ \sf \: 2x - 3y = - 4} - - (2)$

Multiplying equation 1st by 2

We get,

$\boxed{ \sf \: 2x - 2y = - 6} \: - - (3)$

Subtracting Equation 3rd from 2nd!

$\: \: \: \sf \: 2x - 3y = - 4 \\( - ) \: 2x - 2y = - 6 \\ ( \sf \green{ \: sign \: will \: changed})$

____________________

$\sf \: \implies - y = 2 \\ \implies \red{ \boxed{ \sf \green {y = - 2}}}$

Putting the Value of Y in Equation 1st

$\sf \rightarrow \boxed{ \sf \: x - y = - 3} \\ \implies \sf \: x - ( - 2) = - 3 \\ \implies \sf \: x + 2 = - 3 \\ \implies \sf \: x = - 3 - 2 \\ \implies \: \red{ \boxed{ \green{ \: \sf \: \: x = - 5}}}$

According to question

$= ( \sf \: x,y) \\ : \implies \: \boxed{ ( - 5 \: , - 2)}$

••••♪♪