Question

solve the following system of equations for all three variables.
$4x - y - 8z = 5$
$x - y - 8z = -4$
$x + y + 7z = 9$
answer attempt 1 out of 2
$x = \square$ $y = \square$ $z = \square$
submit answer

Explanation:

Step1: Eliminate $y,z$ with Eq1-Eq2

$4x - y - 8z - (x - y - 8z) = 5 - (-4)$
$3x = 9$

Step2: Solve for $x$

$x = \frac{9}{3} = 3$

Step3: Substitute $x=3$ into Eq2

$3 - y - 8z = -4$
$-y - 8z = -7$
$y + 8z = 7$ (Eq4)

Step4: Substitute $x=3$ into Eq3

$3 + y + 7z = 9$
$y + 7z = 6$ (Eq5)

Step5: Eliminate $y$ with Eq4-Eq5

$(y + 8z) - (y + 7z) = 7 - 6$
$z = 1$

Step6: Substitute $z=1$ into Eq4

$y + 8(1) = 7$
$y = 7 - 8 = -1$

Answer:

$x=3$, $y=-1$, $z=1$