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

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

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

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

x = - 4, y = 6, z = 1

Solution steps

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

Isolate

x

for

3 x + 2 y + z = 1 : x = \frac{1 - 2 y - z}{3}

Substitute

x = \frac{1 - 2 y - z}{3}

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

Simplify

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

Isolate

y

for

\frac{- y + 7 z + 5}{3} = 2 : y = 7 z - 1

Substitute

y = 7 z - 1

[\frac{7 z - 1 - 4 z + 1}{3} = 1]

Simplify

[z = 1]

For

y = 7 z - 1

Substitute

z = 1

y = 7 \cdot 1 - 1

Simplify

y = 6

For

x = \frac{1 - 2 y - z}{3}

Substitute

y = 6, z = 1

x = \frac{1 - 2 \cdot 6 - 1}{3}

\frac{1 - 2 \cdot 6 - 1}{3} = - 4

x = - 4

The solutions to the system of equations are:

x = - 4, y = 6, z = 1

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

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

x + y = 7, x - y = 3

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

5 x + 4 y = 4, x - 20 = 20 y

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