Find the 4 variables. Show complete solution

Question

x + 2y +3z = 1. Next is 2y + 3z + 4u = -6. Next x + 3z + 4u = -7. Last is x + 2y + 4u = 3. Show solution using only algebra

Answer 1

x + 2y +3z = 1  ------------------------(i)

2y + 3z + 4u = -6  -------------------------------(ii)

x + 3z + 4u = -7  -------------------------------------(iii)

x + 2y + 4u = 3 ------------------------------------(iv)

Adding all 4 equation together we get:

3x + 6y +9z + 12u = -9

3(x+2y+3z+4u) = -9

x +2y +3z+ 4u= -3  ---------------------------(v)

putting the value of eq(1) in (v) we get:

1 + 4u = -3

or u = -1

similarly, putting the value of eq(ii) in (v) we get:

x - 6 = -3

or x= 3

putting the value of eq(iii) in (v) we get:

2y - 7 =-3

or 2y = 4

or y = 2

Again putting the value of eq(iii) in (v) we get:

3z +3 = -3

or 3z = -6

or z = -2

Comments

x=3

y=2

z= -2

u= -1

Answer 2

(x+2y)+3z=1, (x+2y)+4u=3, so 1-3z=3-4u, 4u=3z+2.

2y+3z+3z+2=-6, 2y+6z+2=-6, y+3z=-4, y=-3z-4.

We now have u and y in terms of z. So we can substitute their values in the last equation: x-6z-8+3z+2=3, x=3z+8+3-2=3z+9.

Now we have u, x, y in terms of z.

x+3z+4u=-7⇒3z+9+3z+3z+2=-7, 9z=-18, z=-2.

Therefore u=(3z+2)/4=-4/4=-1; x=3z+9=-6+9=3; y=-3z-4=6-4=2.

So (u,x,y,z)=(-1,3,2,-2).