What is 2x+y+z=1,6x+2y+z=-1,-2x+2y+z=7 ?

The solution to 2x+y+z=1,6x+2y+z=-1,-2x+2y+z=7 is x=-1,y=2,z=1

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2x+y+z=1,6x+2y+z=-1,-2x+2y+z=7

2 x + y + z = 1, 6 x + 2 y + z = - 1, - 2 x + 2 y + z = 7

x = - 1, y = 2, z = 1

Solution steps

2 x + y + z = 1 6 x + 2 y + z = - 1 - 2 x + 2 y + z = 7

Isolate

x

for

2 x + y + z = 1 : x = \frac{1 - y - z}{2}

Substitute

x = \frac{1 - y - z}{2}

[6 \cdot \frac{1 - y - z}{2} + 2 y + z = - 1 - 2 \cdot \frac{1 - y - z}{2} + 2 y + z = 7]

Simplify

[- y - 2 z + 3 = - 1 3 y + 2 z - 1 = 7]

Isolate

y

for

- y - 2 z + 3 = - 1 : y = - 2 z + 4

Substitute

y = - 2 z + 4

[3 (- 2 z + 4) + 2 z - 1 = 7]

Simplify

[- 4 z + 11 = 7]

Isolate

z

for

- 4 z + 11 = 7 : z = 1

For

y = - 2 z + 4

Substitute

z = 1

y = - 2 \cdot 1 + 4

Simplify

y = 2

For

x = \frac{1 - y - z}{2}

Substitute

y = 2, z = 1

x = \frac{1 - 2 - 1}{2}

\frac{1 - 2 - 1}{2} = - 1

x = - 1

The solutions to the system of equations are:

x = - 1, y = 2, z = 1

x + y + z = 6, x - y + z = 2, x - z = - 2

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

2 x + 3 y = 53, 3 x - y = 19

4 x + 6 y = 2, 6 x + 5 y = 1

5 x - 3 y = - 16, 5 x + 3 y = 2

What is 2x+y+z=1,6x+2y+z=-1,-2x+2y+z=7 ?
The solution to 2x+y+z=1,6x+2y+z=-1,-2x+2y+z=7 is x=-1,y=2,z=1