Question

Solve the following system. Please show me how you did it.

Answer 1

x = 3, y = 4 and z = -5.

Explanation:

Use the elimination method:

-3x + 2y + z = -6...........(1)

x + 3y + 2z = 5..............(2)

4x + 4y + 3z = 13..........(3)

Multiply the first equation by -2:

6x - 4y - 2z = 12 Add this to equation (2):

7x - y = 17...........(4)

Now Multiply equation (2) by 3 and equation (3) by -2

3x + 9y + 6z = 15 ............(5)

-8x - 8y - 6z = -26............(6) Adding (5) + (6):

-5x + y = -11..........(7)

Now Add (7) and (4):

2x = 6

x = 3.

Now substitute for x in (4):

7(3) - y = 17

-y = 17 - 21 = -4

y = 4.

Finally substitute for x and y in equation (3) to find z:

4(3) + 4(4) +3z = 13

3z = 13 - 12 - 16 = -15

z = -5.