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3r-s+4 = -5 -8 cs- 328 20 云=2 14) -5x + 3y + z = 4 -3.x + y+ S = -5 -4x+2y+3=13

User Hosseio
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Problem 14

we have

-5x+3y+6z=4 -------> equation 1

-3x+y+5z=-5 -------> equation 2

-4x+2y+z=13 ------> equation 3

step 1

In the equation 3 isolate the variable z

-4x+2y+z=13

z=-4x-2y+13 --------> equation 4

step 2

Substitute equation 4 in equation 1

-5x+3y+6(-4x-2y+13)=4

-5x+3y-24x-12y+78=4

-29x-9y=-74 ----------> equation 5

step 3

substitute equation 4 in equation 2

-3x+y+5(-4x-2y+13)=-5

-3x+y-20x-10y+65=-5

-23x-9y=-70 -------> equation 6

step 4

Solve the system of equations 5 and 6

-29x-9y=-74 ----------> equation 5

-23x-9y=-70 -------> equation 6

Multiply equation 6 by -1

-1*{-23x-9y=-70} -------> 23x+9y=70 -------> equation 7

step 5

Adds equation 5 and equation 7

-29x-9y=-74

23x+9y=70

--------------------

-6x=-4

x=4/6

x=2/3

step 6

Find the value of y

substitute the value of x in equation 5 or equation 7

User KWondra
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