How do you solve the system y - 2 z = - 6y2z=6, - 4x + y + 4 z = 444x+y+4z=44, - 4 x + 2 z = 304x+2z=30?

1 Answer
Dec 16, 2015

(x,y,z)=(-5,4,5)(x,y,z)=(5,4,5)

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):}