Question

solve by cramers rule X+Y=5, Y+Z=8, Z+X=7​

Answer 1

Answer:

Y = 3

X=2

Z=5

Step-by-step explanation:

Hope it will help you

Answer 2

Given Question:

Solve by Cramer's Rule :-

x + y = 5

y + z = 8

z + x = 7

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$\large\underline\purple{\bold{Solution :- }}$

The given system of equations are

x + y = 5

y + z = 8

z + x = 7

$\begin{gathered}\tt A=\left[\begin{array}{ccc}1&1&0\\0&1&1\\1&0&1\end{array}\right]\end{gathered}$

$\begin{gathered}\tt B=\left[\begin{array}{c}5\\8\\7\end{array}\right]\end{gathered}$

$\begin{gathered}\tt X=\left[\begin{array}{c}x\\y\\z\end{array}\right]\end{gathered}$

$\large\underline{\bold{❥︎Step :- 1 }}$

☆ Now finding |A|

$</p><p> \bf \:  ⟼ |A| = \begin{array}{|ccc|}</p><p>1 & 1 & 0 \\</p><p>0 & 1 & 1 \\</p><p>1 &0 & 1 \\</p><p>\end{array}$

$\bf \:  |A| = 1(1 - 0) - 1(0 - 1)$

$\bf\implies \: |A| = 2$

$\bf\implies \:system \: of \: equation \: have \: unique \: solution$

$\large\underline{\bold{❥︎Step :- 2 }}$

$\bf \:  ⟼ |D_1| = \begin{array}{|ccc|}</p><p>5 & 1 & 0 \\</p><p>8 & 1 & 1 \\</p><p>7 &0 & 1 \\</p><p>\end{array}$

$\bf\implies \: |D_1| = 5(1 - 0) - 1(8 - 7)$

$\bf\implies \: |D_1| = 5 - 1 = 4$

$\large\underline{\bold{❥︎Step :- 3 }}$

$\bf \:  ⟼ |D_2| = \begin{array}{|ccc|}</p><p>1 & 5 & 0 \\</p><p>0 & 8 & 1 \\</p><p>1 &7 & 1 \\</p><p>\end{array}$

$\bf\implies \: |D_2| = 1(8 - 7) - 5(0 - 1)$

$\bf\implies \: |D_2| = 1 + 5 = 6$

$\large\underline{\bold{❥︎Step :- 4 }}$

$\bf \:  ⟼ |D_3| = \begin{array}{|ccc|}</p><p>1 & 1 & 5 \\</p><p>0 & 1 & 8 \\</p><p>1 &0 & 7 \\</p><p>\end{array}$

$\bf\implies \: |D_3| = 1(7 - 0) - 1(0 - 8) + 5(0 - 1)$

$\bf\implies \: |D_3| = 7 + 8 - 5 = 10$

$\large\underline{\bold{❥︎Step :- 5 }}$

$\bf \:  ⟼ x = \dfrac{ |D_1| }{ |A| } = \dfrac{4}{2} = 2$

$\bf \:  ⟼ y = \dfrac{ |D_2| }{ |A| } = \dfrac{6}{2} = 3$

$\bf \:  ⟼ z = \dfrac{ |D_3| }{ |A| } = \dfrac{10}{2} = 5$