PLEASE I NEED HELP

Solve the system of equations.

–5x – 12y – 43z = –136
–4x – 14y – 52z = –146
21x + 72y + 267z = 756

Question options:

x = 6, y = 9, z = –6

x = 1, y = 3, z = 4

infinite solutions

no solution

no solution

Step-by-step explanation:

–5x – 12y – 43z = –136

–4x – 14y – 52z = –146

21x + 72y + 267z = 756

Every coefficient of the second equation is a multiple of 2, so divide both sides by 2.

Every coefficient of the third equation is a multiple of 3, so divide both sides by 3.

–5x – 12y – 43z = –136

–2x – 7y – 26z = –73

 7x + 24y + 89z = 252

Let's call the above system the "simplified original system."

Using the simplified original system, multiply the first equation by -2 and the second equation by 5. Then add them.

          10x + 24y + 86z = 272

(+)      -10x - 35x - 130z = 365

                   -11y - 44z = 637

Now we have an equation with only y and z.

Now, using the simplified original system, multiply the second equation by 7 and the third equation by 2. Then add them.

        –14x – 49y – 182z = –511

(+)       14x + 48y + 178z = 504

                     -y - 4z = -7

Now we have a system in 2 unknowns, y and z.

-11y - 44z = 637

-y - 4z = -7

Multiply the second equation by -11 and add to the first equation.

      -11y - 44z = 637

(+)     11y + 44z = 77

                 0 = 714

Since 0 = 714 is false, this system has no solution.

No solution

Step-by-step explanation:

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

step-by-step explanation:

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