1 Solve the system of equations xy4z 4 0 x z 3 and y 3z

#1 Solve the system of equations. x-y+4z =-4 0 x ; z + 3, and y = 3z + 1, where z is any real number or{(x, y, z) lx = z + 3, and y = 3z + 1.where z is any real number) xz-3 . z, and y 3x + 1, where z is any real number or {(x, y, z) lx =-3-z, and y-3z + 1, where z 1s any real number) Ox=3z + 1.and y = z-3, where z is any real number or {(x, y, z) lx-3z + 1, and y = z-3, where z 1s any real number) O inconsistent

Solution

1) 2x -y +5z = -7 ---(1)

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

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

Fromequation 2 and 3 : add the two equations

2x +2z = -6

x = -z -3

Now substitute value of x in 1 st equation:

2( -z -3) -y +5z =-7

-2z -6 -y +5z = -7

-y +3z = -1

y = 3z +1

So, x = -z -3 , y = 3z +1 where z is any rea number

2)

x^2 +y^2 = 106

x^2 - y^2 = -56

solve by eleimnation:

add the two equations:

2x^2 = 50

x^2 = 25

x= +5 , -5

y^2 = 106 - 25 = 81

y = 9 , -9

Solution : ( 5, 9) ( 5, -9) , ( -5, 9) ( -5, -9)