Question

prove that the following set of equations are 3x+3y+2z=1,x+2y=4,10y+3z=-2,2x-3y-z=5​

Answer 1

x = 2 , y = 1, z = - 4

Step-by-step explanation:

3x+3y+2z = 1 ......................( 1 )

x+2y = 4 ......................( 2 )

10y+3z = -2 ......................( 3 )

2x-3y-z = 5 ......................( 4 )

Now,

(1) + (4) ⇒ 3x+3y+2z + 2x-3y-z = 1+5

⇒5x + z = 6 ......................( 5 )

From ( 2)

x = 4 - 2y

Substituting the value of x in (5) we get

5(4-2y) + z = 6

-10y + z = - 14 .................(7)

Now

(3) + (7)⇒10y+3z - 10y + z = - 2 - 14

⇒4z = -16

⇒z = - 4

Putting the value of z in (7)

-10y - 4 = -14

⇒y = 1

Putting the value of y in (2)

x = 2

∴ (x, y, z) = (2, 1, -4)