Question

Can someone help me with this

2x+4y+3z=6
x-2y+z=-5
-x-3y-2z=-7
solve for x,y,z

Answer 1

x = -7 2/3, y = 1 1/3 and z = 5 1/3.

Explanation:

2x+4y+3z=6 ..... 1

x-2y+z=-5 ...... 2

-x-3y-2z=-7 .......3

Add equations 2 and 3 to eliminate x:

-5y - z = -12 .....4

Multiply equation 2 by - 2:

-2x + 4y - 2z = 10

Add this to equation 1:

8y + z = 16 ........ 5

Now add equation 4 to equation 5:

3y = 4

y = 4/3 = 1 1/3.

Now find z by substituting for y in equation 4:

-5(4/3) - z = -12

z = 12 - 20/3

z = 36/3 - 20/3 = 16/3 = 5 1/3.

Finally, we find x by substituting for y and z in equation 1:

2x + 4*4/3 + 3*16/3 = 6

2x = 6 - 16/3 - 16

2x = 18/3 - 16/3 - 48/3 = -46/3

x = 23/3 = 7 2/3.