What is 4x+y-2z=-3,3x-y+4z=-2,-x+y+z=5 ?

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

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4x+y-2z=-3,3x-y+4z=-2,-x+y+z=5

4 x + y - 2 z = - 3, 3 x - y + 4 z = - 2, - x + y + z = 5

x = - 1, y = 3, z = 1

Solution steps

4 x + y - 2 z = - 3 3 x - y + 4 z = - 2 - x + y + z = 5

Isolate

x

for

4 x + y - 2 z = - 3 : x = \frac{- 3 - y + 2 z}{4}

Substitute

x = \frac{- 3 - y + 2 z}{4}

[3 \cdot \frac{- 3 - y + 2 z}{4} - y + 4 z = - 2 - \frac{- 3 - y + 2 z}{4} + y + z = 5]

Simplify

[\frac{- 7 y + 22 z - 9}{4} = - 2 \frac{5 y + 2 z + 3}{4} = 5]

Isolate

y

for

\frac{- 7 y + 22 z - 9}{4} = - 2 : y = - \frac{- 22 z + 1}{7}

Substitute

y = - \frac{- 22 z + 1}{7}

[\frac{5 ( - \frac{- 22 z + 1}{7} ) + 2 z + 3}{4} = 5]

Simplify

[\frac{31 z + 4}{7} = 5]

Isolate

z

for

\frac{31 z + 4}{7} = 5 : z = 1

For

y = - \frac{- 22 z + 1}{7}

Substitute

z = 1

y = - \frac{- 22 \cdot 1 + 1}{7}

- \frac{- 22 \cdot 1 + 1}{7} = 3

y = 3

For

x = \frac{- 3 - y + 2 z}{4}

Substitute

y = 3, z = 1

x = \frac{- 3 - 3 + 2 \cdot 1}{4}

\frac{- 3 - 3 + 2 \cdot 1}{4} = - 1

x = - 1

The solutions to the system of equations are:

x = - 1, y = 3, z = 1

2 x + 5 y = 1, - x + y = 3

x + y = 10, y - x = 8

x - 5 y = 10, 3 x + y = 6

5 x - 9 y = 2, x + 4 y = 1

5 x + y = 9, x - 2 y = 4

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