Algebraically solve the system of equations using any method you wish. x-3y+ 8z-

Question

Algebraically solve the system of equations using any method you wish. x-3y+ 8z-2 2x+ 5y -4z 21 5x- 4y 35 Select the correct choice below and fill in any answer boxes within your choice. O A. The solution is(Simplty your answers.) ) B. There are infinitely many solutions. Using ordered triplets, the solution can be written as {(x,y,z) | x = , y= , 2 any real number (Simplify your answers. Type expressions using z as the variable as needed. Do not factor.) There are infinitely many solutions. Using ordered triplets, the solution can be written as (x.yz)y ay real number, z any real number (Simplify your answer. Type an expression using y and z as the variables as needed. Do not factor.) C.

Explanation / Answer

given equations

x-3y +8z=2--------------->(a)

-2x+5y-4z=21 ,multiply by 2 =>-4x+10y -8z=42----------------->(b)

5x-4y =-35---------------------->(c)

add (a) and (b)

=>x-3y +8z-4x+10y -8z=2+42

=>-3x+7y =44

=>x=(7y-44)/3------------->(d)

put (d) in (c)

=>5((7y-44)/3)-4y =-35

=>((35y-220)/3)-4y =-35

=>(35y-220)-12y =-105

=>23y =115

=>y = 5

x=(7y-44)/3,y=5

=>x=(7*5 -44)/3

=>x=-3

x-3y +8z=2 ,x=-3 , y=5

=>-3-15 +8z=2

=>8z= 20

=>z=5/2

A.The solution set is (-3,5, 5/2)

A.The solution set is (-3,5, 2.5)

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