Question

Solve the following system. If the system's equations are dependent or if there is no solution, state this.- 4x + 9y + 3z = 4X+ 5y + 6z = 45x - 4y + 3z = 0Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer 1

- 4x + 9y + 3z = 4 (a)

X+ 5y + 6z = 4 (b)

5x - 4y + 3z = 0 (c)

Multiply (b) by 5, then subtract (c) from (b)

5x + 25y + 30z = 20

-

5x -4y +3z = 0

_______________

29y + 27z = 20 (d)

Multiply (b) by 4, then add (a) and (b)

-4x + 9y + 3x = 4

+

4x + 20y + 24z = 16

_______________

29y +27y = 20 (e)

Now we have a system of 2 equations (d) and (e)

29y + 27z = 20 (d)

29y +27y = 20 (e)

Since both equations are the same, there are infinite solutions.

the system is dependent