Question

Solve the system of equations.

3x – 2 = –18 + 5y
8y – 6 = 4x + 9y
y – 10 = 3x + 2z

A. (–1, –4, –8)
B. (–2, 11, 7)
C. (–2, 0, –11)
D. (–2, 2, –1)

Answer 1

option D

Explanation:

3x – 2 = –18 + 5y Equation 1

8y – 6 = 4x + 9y Equation 2

y – 10 = 3x + 2z Equation 3

Using Equation 1 we have:

3X=-18+5Y+2

3X=-16+5Y

`X=(-16+5Y)/(3)` Equation 4

Using Equation 3 we have:

Y-10-3X=2Z

So
`Z=(Y-10-3X)/(2)` Equation 5

Using equation 2 and substituting equation 4 we have:

`8Y-6=4((-16+5Y)/(3) )+9Y\\\\8Y-6=(-64)/(3)+(20)/(3)Y+9Y\\\\8Y-9Y-(20)/(3)Y =(-64)/(3)+6\\\\-Y-(20)/(3)Y =(-46)/(3)\\(-23)/(3)Y =(-46)/(3)\\23Y=46\\Y =(46)/(23)=2`

Using Equation 4 we have:

`X=(-16+5*(2))/(3) =(-16+10)/(3)=-2`

Using Equation 5 we have:

`Z=(2-10-3*(-2))/(2) =-1`

Finally:

X=-2

Y=2

Z=-1