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10x+7y-2z=463x-2y+9z=225x+y-3z=28

User Lorine
by
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1 Answer

2 votes

First, eliminate one variable: by adding two equations:

10x+7y-2z=46 (a)

3x-2y+9z=22 (b)

5x+y-3z=28​ (c)

Multiply (c) by 2 and subtract it to (a):

10x+7y-2z= 46

-

10x+2y-6z=56

____________

5y+4z= -10 (1)

Add another 2:

Multiply (c) by 3 and subtract it to (b) multiplied by 5

15x-10y+45z= 110

-

15x+3y-9z= 84

____________

-13y+36z= 26 (2)

Solve the system:

5y+4z= -10 (1)

-13y+36z= 26 (2)

Multiply (1) by 9 and subtract (2) to (1)

45y+36z= -90

-

-13y+36z=26

______________

58y=-116

y= -116/58

y= -2

Replace y on (1)

5(-2)+4z=-10

-10+4z=-10

4z=-10+10

4z=0

z=0

Replace z and y on a, b or c: and solve for x

10x+7y-2z=46 (a)

10x+7(-2)-2(0)= 46

10x-14=46

10x=46+14

10x= 60

x= 60/10

x= 6

solution:

x=6, y=-2 , z=0

User Yunandtidus
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7.3k points