Question

30. What is the solution to the system of equations? (1 point)

Answer 1

Answer:

Option B) (-1,7,5) is correct.

The solution to the given system of equation is (-1,7,5)

Step-by-step explanation:

Given system of equations are

$-7x-2y+z=-2\hfill (1)$

$6x-y-z=-18\hfill (2)$

$5x+4y-z=18\hfill (3)$

To find the solution of the given system of equations by using Elimination method:

Now adding equations (1) and (2)

$-7x-2y+z=-2$

$6x-y-z=-18$

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$-x-3y=-20$

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$-x-3y=-20$

$-(x+3y)=-20$

$x+3y=20\hfill (4)$  (since "-" getting cancelled)

Now adding equations (1) and (3)

$-7x-2y+z=-2$

$5x+4y-z=18$

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$-2x+2y=16$

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$-2x+2y=16$

$2(-x+y)=16$

$-x+y=8\hfill (5)$

Now adding equations (4) and (5)

$x+3y=20$

$-x+y=8$

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$4y=28$

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$y=\frac{28}{4}$

Therefore y=7

Substituting y=7 in equation (4)

$x+3y=20$

$x+3(7)=20$

$x+21=20$

$x=20-21$

Therefore x=-1

Now substituting the values x=-1 and y=7 in equation (1) we get

$-7x-2y+z=-2$

$-7(-1)-2(7)+z=-2$

$7-14+z=-2$

$z=-2+7$

Therefore z=5

Therefore the solution to the given system of equation is (-1,7,5)

Therefore Option B) (-1,7,5) is correct.