Question

Solve the 3 × 3 system shown below. Enter the values of x, y, and z.

x + 2y – z = –3 (1)

2x – y + z = 5 (2)

x – y + z = 4 (3)

Answer 1

Answer: x=1, y=-1, z=2

Step-by-step explanation:

Answer 2

Hi....

eq..................................(3)
x - y + z = 4
z = 4 - x + y.......................................eq(4)

now, in eq.. (1) & (2) putting the
value of z i.e [eq no.....................(4)]

eq....................................(2)
2x -y + z = 5
2x -y + (4 - x + y) = 5 [from eq... 4]
2x - y + 4 -x + y = 5
2x - x = 5 - 4 [+y -y = 0]
x=1 ...........................................................eq(5)

eq......................................(1)
x + 2y - z = -3
x + 2y - (4 - x + y) = -3 [from eq... 4]
x + 2y - 4 + x - y = -3
2x + y = -3 + 4
2x + y = 1
2(1) + y = 1 [from eq... 5]
y = 1-2
y=-1...........................................................eq(6)

now, putting the value of x & y in eq... (4)
z = 4 - x + y
z = 4 -(1) + (-1) [from eq.. 5 & 6]
z = 4 - 1 - 1
z = 4 - 2
z = 2

Hence, the value of X , Y & Z is 1 , -1 , 2 respectively.

Hope it will help you....!!!!