Solving Systems of Equations using 3 variables & 3 equations.

Question

Hw problem is : 

2x + 3y - z = 12 
4x - y + z = -3 
-2 + 2y + z = 3 

Answer 1

Given system of equations are

2x   + 3y  - z  = 12                     -------------------(1)

4x   -   y  + z    = - 3                   -------------------(2)

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

Add equation(1)  and equation(3)

(1)+(3) ⇒ (2x   + 3y  - z) + ( -2x + 2y  + z )   = 12 + 3

(2x - 2x   + 3y + 2y  - z + z)  = 15

5y = 15  ⇒  y = 15/5

y = 3.

 

Add equation(1)  and equation(2)

(1)+(2) ⇒ (2x  + 3y  - z) + (4x  -  y  + z) = 12 - 3

2x + 4x  + 3y - y - z + z = 9

6x  + 2y = 9

Substitute : y = 3.

6x  + 2(3) = 9  ⇒  6x  + 6 = 9  ⇒  6x = 9 - 6

6x = 3  ⇒  x = 3/6

x = ½.

 

(2) ⇒ 4x - y  + z  = - 3

Substitute : x = 1/2 , y = 3.

4(1/2) - 3 + z  = - 3    ⇒   2 - 3 + z  = - 3

z - 1  = - 3    ⇒    z = - 3 + 1

z = - 2.

Solution : x = ½ , y = 3 , z = -2.