solve the system of equations.$4x + 3y + 6z = 3$$5x + 5y + 6z = 5$$6x + 3y + 6z = 3$a. $(x = 1, y = 0, z =…

solve the system of equations.$4x + 3y + 6z = 3$$5x + 5y + 6z = 5$$6x + 3y + 6z = 3$a. $(x = 1, y = 0, z = -1)$b. $(x = -1, y = 2, z = 1)$c. $(x = 0, y = 1, z = 0)$d. $(x = 2, y = -1, z = 2)$please select the best answer from the choices providedabcd

solve the system of equations.$4x + 3y + 6z = 3$$5x + 5y + 6z = 5$$6x + 3y + 6z = 3$a. $(x = 1, y = 0, z = -1)$b. $(x = -1, y = 2, z = 1)$c. $(x = 0, y = 1, z = 0)$d. $(x = 2, y = -1, z = 2)$please select the best answer from the choices providedabcd

Answer

Explanation:

Step1: Subtract Eq1 from Eq3

Let Equation 1: $4x + 3y + 6z = 3$, Equation 3: $6x + 3y + 6z = 3$ $(6x + 3y + 6z) - (4x + 3y + 6z) = 3 - 3$ $2x = 0$ $x = 0$

Step2: Substitute $x=0$ into Eq1 and Eq2

Equation 1 becomes: $3y + 6z = 3$, simplify to $y + 2z = 1$ Equation 2: $5x + 5y + 6z = 5$ becomes $5y + 6z = 5$

Step3: Solve for $y,z$ with substitution

From simplified Eq1: $y = 1 - 2z$ Substitute into $5y + 6z = 5$: $5(1 - 2z) + 6z = 5$ $5 - 10z + 6z = 5$ $-4z = 0$ $z = 0$ Then $y = 1 - 2(0) = 1$

Answer:

C. $(x = 0, y = 1, z = 0)$