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

The solution to x+2y+z=1,4x+3y+5z=5,3x+y+4z=4 is x=(-7z+2)/5+1,y=-(-z+1)/5

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

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

x = \frac{- 7 z + 2}{5} + 1, y = - \frac{- z + 1}{5}

Solution steps

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

Isolate

x

for

x + 2 y + z = 1 : x = 1 - 2 y - z

Substitute

x = 1 - 2 y - z

[4 (1 - 2 y - z) + 3 y + 5 z = 5 3 (1 - 2 y - z) + y + 4 z = 4]

Simplify

[- 5 y + z + 4 = 5 - 5 y + z + 3 = 4]

Isolate

y

for

- 5 y + z + 4 = 5 : y = - \frac{- z + 1}{5}

Substitute

y = - \frac{- z + 1}{5}

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

Simplify

[4 = 4]

For

x = 1 - 2 y - z

Expressing

x

in terms of

z

x = 1 - 2 (- \frac{- z + 1}{5}) - z

Simplify

1 - 2 (- \frac{- z + 1}{5}) - z : \frac{- 7 z + 2}{5} + 1

x = \frac{- 7 z + 2}{5} + 1

The solutions to the system of equations are:

x = \frac{- 7 z + 2}{5} + 1, y = - \frac{- z + 1}{5}

- 6 x + 5 y = 1, 6 x + 4 y = 10

m = \frac{2}{3}, b = 6

f (x) = 8 x - 7, f (x) = 17

x + y = 24, 3 x + y = 0

- 6 m - 3 n = - 33, 4 m + 2 n = 22

What is x+2y+z=1,4x+3y+5z=5,3x+y+4z=4 ?
The solution to x+2y+z=1,4x+3y+5z=5,3x+y+4z=4 is x=(-7z+2)/5+1,y=-(-z+1)/5