X+Y+Z=0 3x+Y=0 Y-2z=7 I Need Some Help What Is The Answer?

X+y+z=0 3x+y=0 y-2z=7 i need some help what is the answer?

  Answer:

x = -1
y = 3
z = -2

Solution:

x + y + z = 0 (Equation 1)

3x + y = 0 (Equation 2)

y - 2z = 7 (Equation 3)

Solve for x in equation 2:

3x + y = 0 \\ 3x = - y \\ x = \frac{ - y}{3}

Solve for z in equation 3:

y - 2z = 7 \\ - 2z = 7- y \\ z = \frac{ - 7 + y}{2}

Substitute the value of x and z to equation 1:

x + y + z = 0 \\ \frac{ - y}{3} + y + ( \frac{ - 7 + y}{2} ) = 0 \\ - 2y + 6y - 21 + 3y = 0 \\ 7y = 21 \\ y = 3

Substitute the value of y in equation 2 to get the value of x:

3x + y = 0 \\ 3x + 3 = 0 \\ 3x = - 3 \\ x = - 1

Substitute the value of y in equation 3 to get the value of z:

y - 2z = 7 \\ 3 - 2z = 7 \\ - 2z = 4 \\ z = - 2

Check:

x + y + z = 0 \\ - 1 + 3 - 2 = 0 \\ 0 = 0

^_^

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