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Chapter 13: Q. 9 (page 870)

Solve the system:x-2y+z=153x+y-3z=-8-2x+4y-z=-27

Short Answer

Expert verified

The solution of the given system:

x=2y=-5z=3

Step by step solution

01

Step 1. Given information.

System of equations:

x-2y+z=15.........equation(1)3x+y-3z=-8...........equation(2)-2x+4y-z=-27...........equation(3)
02

Step 2. Add equation (1) and (3)

x-2y+z-2x+4y-z=15-27-x+2y=-12

x-2y=12..........equation(4)

03

Step 3. Substitute the value of equation (4) in to the equation (1).

12+z=15z=15-12z=3

04

Step 4. Substitute value of z into the equation (2).

3x+y-3脳3=-83x+y-9=-83x+y=9-83x+y=1

y=1-3x...........equation (5)

05

Step 5. Substitute the value of y from equation (5) into the equation (4).

x-2(1-3x)=12x-2+6x=127x-2=127x=12+27x=14x=147x=2

06

Step 6. Substitute the value of x into the equation (5).

y=1-3脳2y=1-6y=-5

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