Im not sure how to solve this type of system. Can someone please explain how its supossed to be solved.

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1 Answer

2x + 5y - 3z = -5

3x + 2y + 7z = 15

5x - 4y + 6z = 34

multiply the top equation by 2 on both sides

4x + 10y - 6z = -10

3x + 2y + 7z = 15

5x - 4y + 6z = 34

add the bottom equation to the top equation

9x + 6y + 0z = 24

3x + 2y + 7z = 15

5x - 4y + 6z = 34

multiply the middle equation by 6 on both sides and the bottom equation by -7 on both sides

9x + 6y + 0z = 24

18x + 12y + 42z = 90

-35x + 28y - 42z = -238

add the bottom equation to the middle equation.

9x + 6y + 0z = 24

-17x + 40y + 0z = -148

-35x + 28y - 42z = -238

mutiply the top equation by 20 on both sides and the middle equation by -3 on both sides

180x + 120y + 0z = 480

51x - 120y + 0z = 444

-35x + 28y - 42z = -238

add the middle equation to the top equation

231x + 0y + 0z = 924

51x - 120y + 0z = 444

-35x + 28y - 42z = -238

divide the top equation by 231 on both sides

x + 0y + 0z = 924/231

51x - 120y + 0z = 444

-35x + 28y - 42z = -238

reduce 924/231

x + 0y + 0z = 4

51x - 120y + 0z = 444

-35x + 28y - 42z = -238

Now we know x = 4

Let's plug x = 4 into the middle equation:

204 - 120y + 0z = 444

-120y = 220

y = -220/120

y = -11/6

Now we know y = -11/6

Let's plug x = 4 and y = -11/6 into the bottom equation:

-140 - 308/6 - 42z = -238

-140 - 154/3 - 42z = -238

-520 - 154 - 126z = -714

-674 - 126z = -714

126z = -40

z = -40/126

z = -20/63

Answer:  (4, -11/6, -20/63)
by Top Rated User (103k points)

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