Question

Given the system of equations 2 x − 3 y − 9 z = 9 x + 3 z = 3 − 3 x + y − 4 z = − 10 (a) determine whether the system is inconsistent or dependent; Your answer is (input inconsistent or dependent) dependent Correct (b) if your answer is dependent in (a), find the complete solution. Write x and y as functions of z .

Answer 1

Answer:

Dependent

$x=3-3z$

$y=-5z-1$

Step-by-step explanation:

We are given that system of equations

$2x-3y-9z=9$ (Equation I)

$x+3z=3$ ( Equation II)

$-3x+y-4z=-10$ (Equation III)

Equation III multiply by 3 and then add to equation I then we get

$-7x-21z=-21$

Divided by -7 then we get

$x+3z=3$

Now , obtained equation subtract from equation II then we get

0=0

Hence, equation II is a linear combination of equation I and equation III.

Therefore, system is dependent because system has infinite solutions.

$x=3-3z$

Substitute the value of x in equation I then we get

$2(3-3z)-3y-9z=9$

$6-6z-3y-9z=9$

$3y=-15z+6-9=-15z-3$

$y=-5z-1$