What is x+y+z=1,x+2y+3z=6,x+3y+4z=6 ?

The solution to x+y+z=1,x+2y+3z=6,x+3y+4z=6 is x=1,y=-5,z=5

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

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

x = 1, y = - 5, z = 5

Solution steps

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

Isolate

x

for

x + y + z = 1 : x = 1 - y - z

Substitute

x = 1 - y - z

[1 - y - z + 2 y + 3 z = 6 1 - y - z + 3 y + 4 z = 6]

Simplify

[y + 2 z + 1 = 6 2 y + 3 z + 1 = 6]

Isolate

y

for

y + 2 z + 1 = 6 : y = - 2 z + 5

Substitute

y = - 2 z + 5

[2 (- 2 z + 5) + 3 z + 1 = 6]

Simplify

[- z + 11 = 6]

Isolate

z

for

- z + 11 = 6 : z = 5

For

y = - 2 z + 5

Substitute

z = 5

y = - 2 \cdot 5 + 5

Simplify

y = - 5

For

x = 1 - y - z

Substitute

y = - 5, z = 5

x = 1 - (- 5) - 5

Simplify

x = 1

The solutions to the system of equations are:

x = 1, y = - 5, z = 5

254 x + 309 y = - 55, 309 x + 254 y = 55

x + 4 y = 5, x + 10 y = 11

p = 2, q = 1

0.4 x - 0.7 y = - 13, 0.6 x + 0.7 y = 33

- 3 (2 x - 6) = 42, - 6 x + 18 = 42, - 6 x = 24, x = - 4

What is x+y+z=1,x+2y+3z=6,x+3y+4z=6 ?
The solution to x+y+z=1,x+2y+3z=6,x+3y+4z=6 is x=1,y=-5,z=5