How do you solve this system of equations: #4x + y + 8z = 6 , 7x - y = 9z = - 10 , and - 6x + y - 8z = 8#?

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Answer 1 · 2017-10-16T03:27:46

#x=-5#
#y=2#
#z=3#

We're given 3 equations:

#(1) " " 4x + y + 8z = 6#

#(2) " " 7x - y + 9z = -10#

#(3) " " -6x + y - 8z = 8#

Let's create two new equations:

#(1) + (2) = (4) " "" "11x + 17z = -4#

#(2) + (3) = (5) " "" "x + z = -2#

Now, we can multiply equation #(5)# by 11, and then subtract it from #(4)#. This will let us solve for #z#:

#(4) - 11xx(5)#

#[11x + 17z = -4] - [11x + 11z = -22]#

#[6z = 18]#

#z = 3#

Now that we know what #z# is, we can plug it back into another equation (let's use equation #(5)# for convenience) and solve for #x#:

#x + z = -2#

#x + 3 = -2#

#x = -5#

Now that we know what #x# is, we can plug #x# and #z# into another equation (let's use equation #(1)#) and solve for #y#:

#4x + y + 8z = 6#

#4(-5) + y + 8(3) = 6#

#-20 + y + 24 = 6#

#y = 2#

Therefore, the solution to our system of equations is:

#x=-5#
#y=2#
#z=3#

Final Answer