Question

8. Solve this system of equations

4x − 2y + 3z = 1
x + 3y − 4z = −7
3x + y +2z = 5
Select the appropriate response:

A) x = − 1, y = 2, z = 3
B) x = − 1, y = 4, z = 4
C) x = − 3, y = 2, z = 3
D) x = − 1, y = 4, z = 3

Answer 1

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

Explanation:

4x − 2y + 3z = 1

x + 3y − 4z = −7

3x + y +2z = 5

x = 4z - 3y - 7

4(4z - 3y - 7) - 2y + 3z = 1

19z - 14y = 29

3(4z - 3y - 7) + y + 2z = 5

14z - 8y = 26

7z - 4y = 13

y = (7z - 13)/4

19z -14(7z - 13)/4 = 29

-11z/2 = -33/2

z = 3

y = (21-13)/4 = 2

x = 4(3) - 3(2) - 7 = -1

Answer 2

A) x = − 1, y = 2, z = 3

Explanation:

4x − 2y + 3z = 1

x + 3y − 4z = −7

3x + y +2z = 5

Lets eliminate x by multiplying the second equation by -4

4x − 2y + 3z = 1

-4x - 12y + 16z = 28

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

-14y +19z = 29

Lets eliminate x by multiplying the second equation by -3

-3x + -9y +12z = 21

3x + y +2z = 5

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

-8y +14z =26

We now have 2 equations and 2 unknowns

-14y +19z = 29

-8y +14z = 26 Divide this by 2 = -4y +7z = 13

Multiplying the first equation by 4 and the second by -14

-56y +76z =116

56y -98z = -182

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

-22z =-66

Divide each side by -22

-22z/-22 = -66/-22

z=3

Now we need to find y

-14y +19z = 29

-14y +19(3) =29

-14y+ 57 = 29

-14y =29-57

-14y =-28

y =2

Now we need to find x

x + 3y − 4z = −7

x + 3(2) -4(3) =-7

x+6 -12 =-7

x-6 = -7

x = -1