solve the system of equations.$2x + 4y + 3z = 6$$5x + 8y + 6z = 4$$4x + 5y + 2z = 6$a. $(x = -7, y = 9, z =…

solve the system of equations.$2x + 4y + 3z = 6$$5x + 8y + 6z = 4$$4x + 5y + 2z = 6$a. $(x = -7, y = 9, z = -7)$b. $(x = -8, y = 10, z = -6)$c. $(x = -9, y = 11, z = -5)$d. $(x = -6, y = 8, z = -4)$please select the best answer from the choices providedabcd

solve the system of equations.$2x + 4y + 3z = 6$$5x + 8y + 6z = 4$$4x + 5y + 2z = 6$a. $(x = -7, y = 9, z = -7)$b. $(x = -8, y = 10, z = -6)$c. $(x = -9, y = 11, z = -5)$d. $(x = -6, y = 8, z = -4)$please select the best answer from the choices providedabcd

Answer

Explanation:

Step1: Eliminate z from Eq1 and Eq2

Multiply Eq1 by 2: $4x + 8y + 6z = 12$ Subtract Eq2: $(4x+8y+6z)-(5x+8y+6z)=12-4$ Simplify: $-x = 8 \implies x = -8$

Step2: Substitute x=-8 into Eq1 and Eq3

Eq1 becomes: $2(-8)+4y+3z=6 \implies -16+4y+3z=6 \implies 4y+3z=22$ (Eq4) Eq3 becomes: $4(-8)+5y+2z=6 \implies -32+5y+2z=6 \implies 5y+2z=38$ (Eq5)

Step3: Solve for y from Eq4 and Eq5

Multiply Eq4 by 2: $8y + 6z = 44$ Multiply Eq5 by 3: $15y + 6z = 114$ Subtract: $(15y+6z)-(8y+6z)=114-44$ Simplify: $7y=70 \implies y=10$

Step4: Substitute y=10 into Eq4

$4(10)+3z=22 \implies 40+3z=22$ Simplify: $3z=22-40=-18 \implies z=-6$

Answer:

b. $(x=-8, y=10, z=-6)$