Question

Find the value of x, y, z if [(2x+y, x-y)(x-z, x+y+z)] = [(10,-1)(2,8)].

Answer 1

According to the question,
2x+y=10.....eq. 1
x-y= -1........eq. 2
x-z= 2........eq.3
x+y+z= 8...eq.4

Now from eq.2,
y=x+1.

Substituting y=x+1 in eq. 1, we get
2x+x+1=10
=> 3x= 10-1
=> 3x= 9
=> x= 9/3
=> x= 3

Substituting x=3 in eq. 2,
3-y= -1
=> -y= -1-3
=>-y = -4
=> y= 4

Substituting x =3 in eq.3,
3-z=2
=>z=3-2 (changing sides)
=>z= 1
-------x------
Proof:
x+y+z =3+4+1 = 8