Question

Solve for x, y, and z

2x - y + 3z= 10

-3x + y - 2z= -11

-4x + y - 4z = -15

a) (-2, -23, -3)

b) (2, -9, -1)

c) (2, -3, 1)

d) (2, -6, 0)

Answer 1

2x - y + 3z= 10  --------> equation 1

-3x + y - 2z= -11   --------> equation 2

-4x + y - 4z = -15  --------> equation 3

Add first and second equation

2x - y + 3z= 10  

-3x + y - 2z= -11    

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-x + z = -1 -----------------> equation 4

Add first and third equation

2x - y + 3z= 10  

-4x + y - 4z = -15

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-2x - z = -5 -----------------> equation 5

Now add equation 4  and 5

-x + z = -1

-2x - z = -5

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-3x = -6

Divide both sides by -3

so x= 2

We use equation 4  and solve for z

-x + z = -1

-2 + z = -1

Add 2 on both sides

z = 1

Now plug in x=2  and z=1 in any one of the original equation

2x - y + 3z= 10

2(2) - y + 3(1)= 10

4 - y +3 = 10

7 - y = 10

subtract 7 on both sides

-y = 3

y = -3

x=2, y=-3, z= 1

Solution is (2,-3, 1)

Answer 2

solve by linear combination

use 1st equation to cancel y's in 2nd and 3rd equations

add 1st equation to 2nd equation to get

-x+z=-1

add 1st equation to 3rd equation to get

-2x-z=-5

now add the 2 new equations -x+z=-1 and -2x-z=-5 to get

-3x=-6

x=2

sub back

-x+z=-1

-2+z=-1

z=1

sub back

-3x+y-2z=-11

-3(2)+y-2(1)=-11

-6+y-2=-11

y=-3

(x,y,z)=(2,-3,1)

C is answer