Question

solve equation by cramer's rule:7x+7y-7z=2,-x+11y+7z=1,11x+5y+7z=0

Answer 1

Answer:

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Answer 2

Answer:

The solutions to the system of equations By using cramers rules are$x=0, y=\frac{1}{6}, z=-\frac{5}{42}$

Step-by-step explanation:

Cramer's rule is a formula for solving a system of linear equations with as many equations as unknowns that is effective whenever the system has a unique solution.

Given:

• 7x+7y-7z=2,
• -x+11y+7z=1,
• 11x+5y+7z=0

$\left[\begin{array}{c}7 x+7 y-7 z=2 \\-x+11 y+7 z=1 \\11 x+5 y+7 z=0\end{array}\right]$

Matrix of Coefficients

$M=\left(\begin{array}{ccc}7 & 7 & -7 \\-1 & 11 & 7 \\11 & 5 & 7\end{array}\right)$

Answers column:

$\left(\begin{array}{l}2 \\1 \\0\end{array}\right)$

Replace the $x$-column values with the answer-column values

$M_{x}=\left(\begin{array}{ccc}2 & 7 & -7 \\1 & 11 & 7 \\0 & 5 & 7\end{array}\right)$

Replace the $y$-column values with the answer-column values

$M_{y}=\left(\begin{array}{ccc}7 & 2 & -7 \\-1 & 1 & 7 \\11 & 0 & 7\end{array}\right)$

Replace the $z$-column values with the answer - column values

$M_{z}=\left(\begin{array}{ccc}7 & 7 & 2 \\-1 & 11 & 1 \\11 & 5 & 0\end{array}\right)$

Find the derteminant

$\begin{aligned}&D=1764 \\&D_{x}=0 \\&D_{y}=294 \\&D_{z}=-210\end{aligned}$

Solve by using Cramer Rule

$x=\frac{D_{x}}{D}, y=\frac{D_{y}}{D}, z=\frac{D_{z}}{D}$

D denotes the determinant

$x=\frac{D_{x}}{D}=\frac{0}{1764}$

Simplify

$x=0$

$y=\frac{D_{y}}{D}=\frac{294}{1764}$

Simplify $\frac{294}{1764}:$

$z=\frac{D_{z}}{D}=\frac{-210}{1764}$

Simplify $\frac{-210}{1764}: \quad-\frac{5}{42}$

The solutions to the system of equations are:

$x=0, y=\frac{1}{6}, z=-\frac{5}{42}$