# How do you solve the system y - 2 z = - 6, - 4x + y + 4 z = 44, - 4 x + 2 z = 30?

Dec 16, 2015

$\left(x , y , z\right) = \left(- 5 , 4 , 5\right)$

#### Explanation:

Given:
{: ([1],color(white)("XXX"),,y,-2z," = ",-6), ([2],color(white)("XXX"),-4x,+y,+4z," = ",44), ([3],color(white)("XXX"),-4x,,+2z," = ",30) :}

Subtract [3] from [2]
{:([4],color(white)("XXX"),color(white)("XXX"),y,+2z," = ",14):}

Subtract [1] from [4]
{:([5],color(white)("XXX"),color(white)("XXX"),color(white)("XX"),+4z," = ",20):}

Divide [5] by $4$
{:([5],color(white)("XXX"),color(white)("XXX"),color(white)("XX"),z," = ",5):}

Substitute $5$ for $z$ in [1]
{:([6],color(white)("XXX"),color(white)("XXX"),y,-2(5)," = ",-6):}

Add $10$ to both sides of [6]
{:([7],color(white)("XXX"),color(white)("XXX"),y,color(white)("XX")," = ",4):}

Substitute $5$ for $z$ in [3]
{:([8],color(white)("XXX"),-4x,color(white)("XX"),+2(5)," = ",30):}

Simplify
{:([9],color(white)("XXXXX"),x,color(white)("XX"),color(white)("XX")," = ",-5):}