Question

using the following condition prepare to equations and solve

D= |5 7| and Dy= |5 4|
|2 -3| |2 -10|​

Answer 1

Answer:

this is your answer dear...hope it becomes helpfull

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{D = \begin{vmatrix} 5 & \: 7 \\ 2 & - 3 \end{vmatrix} \: \: and \: \: D_y = \begin{vmatrix} 5 & 4 \\ 2& - 10 \end{vmatrix} }$

TO DETERMINE

The value of x and y

EVALUATION

Here it is given that

$\displaystyle \sf{D = \begin{vmatrix} 5 & \: 7 \\ 2 & - 3 \end{vmatrix} \: \: and \: \: D_y = \begin{vmatrix} 5 & 4 \\ 2& - 10 \end{vmatrix} }$

Now

$\displaystyle \sf{D = \begin{vmatrix} 5 & \: 7 \\ 2 & - 3 \end{vmatrix} \: = - 15 - 14 = - 29 }$

$\displaystyle \sf{D_y = \begin{vmatrix} 5 & 4 \\ 2& - 10 \end{vmatrix} = - 50 - 8 = - 58}$

Clearly

$\displaystyle \sf{D_x= \begin{vmatrix} 4 & 7 \\ - 10& - 3 \end{vmatrix} }$

Now

$\displaystyle \sf{D_x= \begin{vmatrix} 4 & 7 \\ - 10& - 3 \end{vmatrix} = - 12 + 70 = 58}$

Hence the required solution is

$\displaystyle \sf{x = \frac{D_x}{D} = \frac{58}{ - 29} = - 2 }$

$\displaystyle \sf{y= \frac{D_y}{D} = \frac{ - 58}{ -29} = 2 }$

FINAL ANSWER

Hence the required solution x = - 2 , y = 2

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