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find the value of x in the following system of equation

3x+2x+z=6

x+y+3z=-5

4x+y-z=10

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)
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Given:     (1)     3x + 2y + z = 6

(2)      x + y + 3z = -5

(3)     4x + y - z = 10

Since you are only looking to solve for x in this system of equations, the first step is to eliminate either of the other two variables. Let's try to eliminate y first by multiplying (2) by -2 and adding it to (1):

-2(x + y + 3z = -5)   ==>   -2x - 2y - 6z = 10

-2x - 2y - 6z = 10

+       3x + 2y + z = 6

____________________

x - 5z = 16

Now multiply the (3) by -2 and add it to (1):

-2(4x + y - z = 10)   ==>   -8x - 2y + 2z = -20

-8x - 2y + 2z = -20

+      3x + 2y + z = 6

___________________

-5x + 3z = -14

Now we take the system of the two new equations we created and eliminate the z variable to solve for x:

(1*)         x - 5z = 16

(2*)     -5x + 3x = -14

To eliminate z, first multiply (1*) by 3 and multiply (2*) by 5:

(1*)     3(x - 5z = 16)        ==>   3x - 15z = 48

(2*)     5(-5x + 3z = -14)   ==>   -25x + 15z = -70

Solve for x by combining these two equations:

3x - 15z = 48

+      -25x + 15z = -70

_____________________

-22x = -22

==>     (-22x)/-22 = (-22)/-22

x = 1

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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3x+2y+z=6 ......  (1) <==Is this what you meant?

x+y+3z=-5 ....... (2)

4x+y-z=10 ...... (3)

(3)-(2): 3x - 4z = 15 ....... (4)

(1)-2*(2): x-5z = 16 ......(5)

(4)-3*(5): 11z = -33

z = -3

x = 16+5z = 1

y = z-4x = -1-4 = -5