What is 3x+2x+z=6,3x+y+z=5,x+y+z=3 ?

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

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3x+2x+z=6,3x+y+z=5,x+y+z=3

3 x + 2 x + z = 6, 3 x + y + z = 5, x + y + z = 3

x = 1, y = 1, z = 1

Solution steps

3 x + 2 x + z = 6 3 x + y + z = 5 x + y + z = 3

Isolate

x

for

3 x + 2 x + z = 6 : x = \frac{6 - z}{5}

Substitute

x = \frac{6 - z}{5}

[3 \cdot \frac{6 - z}{5} + y + z = 5 \frac{6 - z}{5} + y + z = 3]

Simplify

[y + \frac{18 + 2 z}{5} = 5 y + \frac{6 + 4 z}{5} = 3]

Isolate

y

for

y + \frac{18 + 2 z}{5} = 5 : y = 5 - \frac{18 + 2 z}{5}

Substitute

y = 5 - \frac{18 + 2 z}{5}

[5 - \frac{18 + 2 z}{5} + \frac{6 + 4 z}{5} = 3]

Simplify

[5 + \frac{2 z - 12}{5} = 3]

Isolate

z

for

5 + \frac{2 z - 12}{5} = 3 : z = 1

For

y = 5 - \frac{18 + 2 z}{5}

Substitute

z = 1

y = 5 - \frac{18 + 2 \cdot 1}{5}

5 - \frac{18 + 2 \cdot 1}{5} = 1

y = 1

For

x = \frac{6 - z}{5}

Substitute

y = 1, z = 1

x = \frac{6 - 1}{5}

Simplify

x = 1

The solutions to the system of equations are:

x = 1, y = 1, z = 1

x + 2 y = 7, 2 x + 3 y = 0

6 x - 3 y + 10 = 0, 2 - y + 9 = 0

2 y - x = 8, 5 y - x = 1, 4 y - 2 x = 1

2 a + 3 b = 16, 2 a + 8 b = 26

x - y = 2, 2 x + y = 8

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