Question

question 3 of 5
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar(s).
consider this system of linear equations.
$2x + y - z = 8$
$x + z = -5$
$2y - 3z = 21$
the value of x in this linear system is

Explanation:

Step1: Isolate x from Eq2

$x = -5 - z$

Step2: Isolate y from Eq3

$2y = 21 + 3z \implies y = \frac{21 + 3z}{2}$

Step3: Substitute x,y into Eq1

$2(-5 - z) + \frac{21 + 3z}{2} - z = 8$

Step4: Eliminate denominator, simplify

Multiply all terms by 2:
$2*2(-5 - z) + 21 + 3z - 2z = 16$
$-20 - 4z + 21 + 3z - 2z = 16$
Combine like terms:
$1 - 3z = 16$

Step5: Solve for z

$-3z = 16 - 1 = 15 \implies z = -5$

Step6: Find x using z=-5

$x = -5 - (-5) = -5 + 5 = 0$

Answer:

0