AT&T; LTE 8:33 PM math.mcneese.edu 26% [ (1 point) Solve the system using elimin

Question

AT&T; LTE 8:33 PM math.mcneese.edu 26% [ (1 point) Solve the system using elimination -4x-y+ z = 19 How many solutions are there to this system? A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E. Infinitely many F None of the above If there is one solution, give its coordinates in the answer spaces below If there are infinitely many solutions, enter z in the answer blank for z, enter a formula for y in terms of in the answer blank for yand enter a formula for zl in terms of 2in the answer blank for x If there are no solutions, leave the answer blanks for x, yl and empty

Explanation / Answer

Given system of equations are x+y+4z=3

-4x-y+z=19

-5x-4y+6z=36

Solving for x,y,z by using elimination method:

Multiply first equation by 4 and add with second equation,

4x+4y+16z=12

-4x-y+z=19

Addition of above two equations is 3y+17z=31

Multiply first equation by 5 and add with third equation,

5x+5y+20z=15

-5x-4y+6z=36

Addition of above two equations is y+26z=51

By solving y+26z=51 and 3y+17z=31 we can get y and z values.

Multiply the above first equation by 3 and then subtract above second equation from it.

3y+78z=153

3y+17z=31

By subtraction, 61z=122

z=2

Substitute z=2 in y+26z=51

y+26(2)=51

y+52=51

y=51-52

y=-1

Substitute y=-1 and z=2 in first equation x+y+4z=3

x-1+4(2)=3

x-1+8=3

x=3+1-8

x=-4

Therefore, the given system of equatiions has one solution and is x= -4, y=-1, z=2

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