Solve the system analytically, then solve the next equation.

Question

Solve the system analytically

2x-5y+5z=13

5x-4y-2z=-36

x-y+4z=35

 

The solution set is {(_,_,_)}

 

Solve this system

3x+3y+z=0

x-3y+2z=-21

8x-2y+3z=-41

 

The solution set is {_} (type an ordered triple)

Answer 1

Which methods are available to you to solve such systems. You can do these with an augmented matrix and row operations, determinants and Cramer's Rule, or use elimination of variables to reduce the system to a fewer number of equations and variables.

 

I will show you the latter method, because I do not know if you know about matrices yet.

 

Label the equations [1], [2], and [3].

 

Eliminate x from [1] and [2], and then from [1] and [3]:

 

-5[1] + 2[2] → 17y -29z = -137

 1[1] – 2[3] →  -3y -3z   = -57 .

 

Now you can solve this system by elimination as well. Label the first equation [4] and the second [5]:

 

3[4] + 17[5] → -138z = -1380 → z = 10 .

 

Plug back into [5] and solve for y:

 

-3y - 3(10) = -57 → -3y -30 = -57 → -3y = -27 → y = 9 .

 

Finally, plug y = 9 and z = 10 into [3] to solve for x:

 

x - 9 + 4(10) = 35

x + 31 = 35

x = 4 .

 

The solution is (4,9,10).

 

I will let another tutor solve the second system, unless you require a different method.