Question

use cramer's rule to solve : 4x-7y=16 , 5x-9y=-7​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

We have two equation given

$4x - 7y = 16$

$5x - 9y = - 7$

Step 1:First we find determinant by using x and y.

$\sf{D = \left|\begin{array}{c c c} 4 & -7 \\ 5 & -9\end{array}\right|}$

$D = - 9 \times 4 - ( - 7 \times 5)$

$D = - 36 - ( - 35) = - 36 + 35$

$\bold{\red{D = - 1}}$

Step 2: Finding$D_{x}$by replacing y and taking constant.

$D_{x}$=$\sf{D = \left|\begin{array}{c c c} 16 & -7 \\ -7 & 9\end{array}\right|}$

$D_{x}= - 9 \times 16 - ( - 7 \times - 7)$

$D_{x}= - 144 - 49 = - 144 + 49$

$\bold{D_{x}= - 95}$

Step 3: Finding $D_{y}$ by replacing X and taking constant.

$D_{y}$=$\sf{D = \left|\begin{array}{c c c} 4 & 16 \\ 5 & -7\end{array}\right|}$

$D_{y} = - 7 \times 4 - (16 \times 5)$

$\bold{D_{y} = - 28 - 80 = - 108}$

step 4: By using Cramer's Rule we will find values of x and y.

$x = \dfrac{D_{x}}{D} = \dfrac{ - 95}{ - 1} = 95$

$y = \dfrac{D_{y}}{D} = \dfrac{ - 108}{ - 1} = 108$

Hence,the values of x and y are ( 95,108 )

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

We have two equation given

$4x - 7y = 16$

$5x - 9y = - 7$

Step 1:First we find determinant by using x and y.

$\sf{D = \left|\begin{array}{c c c} 4 & -7 \\ 5 & -9\end{array}\right|}$

$D = - 9 \times 4 - ( - 7 \times 5)$

$D = - 36 - ( - 35) = - 36 + 35$

$\bold{\red{D = - 1}}$

Step 2: Finding$D_{x}$by replacing y and taking constant.

$D_{x}$=$\sf{D = \left|\begin{array}{c c c} 16 & -7 \\ -7 & 9\end{array}\right|}$

$D_{x}= - 9 \times 16 - ( - 7 \times - 7)$

$D_{x}= - 144 - 49 = - 144 + 49$

$\bold{D_{x}= - 95}$

Step 3: Finding $D_{y}$ by replacing X and taking constant.

$D_{y}$=$\sf{D = \left|\begin{array}{c c c} 4 & 16 \\ 5 & -7\end{array}\right|}$

$D_{y} = - 7 \times 4 - (16 \times 5)$

$\bold{D_{y} = - 28 - 80 = - 108}$

step 4: By using Cramer's Rule we will find values of x and y.

$x = \dfrac{D_{x}}{D} = \dfrac{ - 95}{ - 1} = 95$

$y = \dfrac{D_{y}}{D} = \dfrac{ - 108}{ - 1} = 108$

Hence,the values of x and y are ( 95,108 )