Determine whether the ordered pair is a solution to the given system of linear equations.

(1,2)

a2linetagadaW
2020-10-23
Answered

Determine whether the ordered pair is a solution to the given system of linear equations.

(1,2)

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Benedict

Answered 2020-10-24
Author has **108** answers

Consider the system of equations as:

1)

2)

Verify if ordered pair (1,2) is solution of (1) and (2).

Substitute

Hence, (1,2) satisfies the equation (1).

Substitute

Hence, (1,2) satisfies the equation (2).

Hence, the ordered pair (1,2) is a solution to the given system of linear equations.

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Determine the reduced echelon form of the homogeneous linear system of three equations in variables ${x}_{1},{x}_{2},{x}_{3},{x}_{4},{x}_{5}$ such that ${x}_{1},{x}_{2},{x}_{4}$ are leading variables; ${x}_{3},{x}_{5}$ are free variables and which has solutions

$\left(\begin{array}{c}2\\ -1\\ 1\\ 0\\ 0\end{array}\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\left(\begin{array}{c}-3\\ 2\\ 0\\ -4\\ 1\end{array}\right)$

Determine the reduced echelon form of the homogeneous linear system of three equations in variables ${x}_{1},{x}_{2},{x}_{3},{x}_{4},{x}_{5}$ such that ${x}_{1},{x}_{2},{x}_{4}$ are leading variables; ${x}_{3},{x}_{5}$ are free variables and which has solutions

$\left(\begin{array}{c}2\\ -1\\ 1\\ 0\\ 0\end{array}\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\left(\begin{array}{c}-3\\ 2\\ 0\\ -4\\ 1\end{array}\right)$

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