Math, asked by ravimore121975, 5 months ago

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

Answers

Answered by Flaunt
17

\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 )

Answered by Anonymous
0

\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 )

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