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Solve the system of equations x_1−3x_2+4x_3=-4 3x_1−7x_2+7x3=-8 −4x_1+6x_2−x_3=7

Forms of linear equations
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asked 2020-10-25
Solve the system of equations $$x_1−3x_2+4x_3=-4$$
$$3x_1−7x_2+7x3=-8$$
$$−4x_1+6x_2−x_3=7$$

Answers (1)

2020-10-26

Given:
$$x_1−3x_2+4x_3=-4$$
$$3x_1−7x_2+7x3=-8$$
$$−4x_1+6x_2−x_3=7$$
Step 1
Find the value of $$\delta_1$$ & $$\delta_2$$
$$\delta_1=[[-4,-3,4],[3,-7,7],[-4,6,-1]]$$
=1(7-42)+3(-3+28)+4(18-28)
=-35+75-40
=0
Step 3
$$\delta_1=[[-4,-3,4],[-8,-7,7],[7,6,-1]$$
=-4(7-42)+3(8-49)+(-48+49)
=140-123
$$=21\ne0$$
according to cramers rule if value of is zero and if any one of $$/_\ 1, /_\ 2 or /_\ 3$$ is non zero then the system of linear equations has no solution.
therefore the given system of linear equations has no solution

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