Question

Determine if the values of the variables listed are solutions of the system of equations. {(2x+2y+3z=9),(x-5y+z=21),(6x-4y-2z=27):} x=3,y=-3,z=3;(3,-3,3)

Answer 1

The values of x=3, y=-3, and z=3 are solutions of the system of equations.

Step-by-step explanation:

To determine if the values of the variables listed are solutions of the system of equations, we substitute the given values of x, y, and z into each equation and check if the resulting equations are true.

For the first equation, when we substitute x=3, y=-3, and z=3, we get (2(3)+2(-3)+3(3)=9), which simplifies to (6-6+9=9). This equation is true.

Similarly, when we substitute x=3, y=-3, and z=3 into the second and third equations, we find that (3-5(-3)+3=21) and (6(3)-4(-3)-2(3)=27) are also true. Therefore, the values of x=3, y=-3, and z=3 are solutions of the system of equations.