Question

3.4 systems in 3 variables question 4 of 5 (1 point) | question attempt: 1 of unlimited solve the system. -x + 3y+z=-3 x - 2y - 2z = 8 3x - 4y - z = 6 x = y = z =

Explanation:

Step1: Add first and second equations

$(-x + 3y+z)+(x - 2y-2z)=-3 + 8$
$y - z=5$, so $y=z + 5$

Step2: Substitute $y = z + 5$ into the first and third equations

First - equation: $-x+3(z + 5)+z=-3$, which simplifies to $-x+3z+15 + z=-3$, then $-x+4z=-18$, or $x=4z + 18$
Third - equation: $3x-4(z + 5)-z=6$, which simplifies to $3x-4z-20 - z=6$, then $3x-5z=26$

Step3: Substitute $x = 4z + 18$ into $3x-5z=26$

$3(4z + 18)-5z=26$
$12z+54-5z=26$
$7z=26 - 54$
$7z=-28$
$z=-4$

Step4: Find the value of $y$

Since $y=z + 5$, substituting $z=-4$ gives $y=-4 + 5=1$

Step5: Find the value of $x$

Since $x=4z + 18$, substituting $z=-4$ gives $x=4\times(-4)+18=-16 + 18=2$

Answer:

$x = 2$, $y = 1$, $z=-4$