What is 5x-3y-z=1,x+4y-6z=-1,2x+3y+4z=9 ?

The solution to 5x-3y-z=1,x+4y-6z=-1,2x+3y+4z=9 is x=1,y=1,z=1

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5x-3y-z=1,x+4y-6z=-1,2x+3y+4z=9

5 x - 3 y - z = 1, x + 4 y - 6 z = - 1, 2 x + 3 y + 4 z = 9

x = 1, y = 1, z = 1

Solution steps

5 x - 3 y - z = 1 x + 4 y - 6 z = - 1 2 x + 3 y + 4 z = 9

Isolate

x

for

5 x - 3 y - z = 1 : x = \frac{1 + 3 y + z}{5}

Substitute

x = \frac{1 + 3 y + z}{5}

[\frac{1 + 3 y + z}{5} + 4 y - 6 z = - 1 2 \cdot \frac{1 + 3 y + z}{5} + 3 y + 4 z = 9]

Simplify

[\frac{23 y - 29 z + 1}{5} = - 1 \frac{21 y + 22 z + 2}{5} = 9]

Isolate

y

for

\frac{23 y - 29 z + 1}{5} = - 1 : y = \frac{29 z - 6}{23}

Substitute

y = \frac{29 z - 6}{23}

[\frac{21 \cdot \frac{29 z - 6}{23} + 22 z + 2}{5} = 9]

Simplify

[\frac{223 z - 16}{23} = 9]

Isolate

z

for

\frac{223 z - 16}{23} = 9 : z = 1

For

y = \frac{29 z - 6}{23}

Substitute

z = 1

y = \frac{29 \cdot 1 - 6}{23}

Simplify

y = 1

For

x = \frac{1 + 3 y + z}{5}

Substitute

y = 1, z = 1

x = \frac{1 + 3 \cdot 1 + 1}{5}

Simplify

x = 1

The solutions to the system of equations are:

x = 1, y = 1, z = 1

x + 3 y = 6, 5 x - 2 y = 13

49 x + 51 y = 499, 51 x + 49 y = 501

x + y = 4, x - y = 2

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

3 x - 4 y = - 7, 5 x - 2 y = 0

What is 5x-3y-z=1,x+4y-6z=-1,2x+3y+4z=9 ?
The solution to 5x-3y-z=1,x+4y-6z=-1,2x+3y+4z=9 is x=1,y=1,z=1