What is 2x+3y+4z=3,2x+6y+8z=5,4x+9y-4z=4 ?

The solution to 2x+3y+4z=3,2x+6y+8z=5,4x+9y-4z=4 is x= 1/2 ,y= 1/3 ,z= 1/4

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2x+3y+4z=3,2x+6y+8z=5,4x+9y-4z=4

2 x + 3 y + 4 z = 3, 2 x + 6 y + 8 z = 5, 4 x + 9 y - 4 z = 4

x = \frac{1}{2}, y = \frac{1}{3}, z = \frac{1}{4}

Solution steps

2 x + 3 y + 4 z = 3 2 x + 6 y + 8 z = 5 4 x + 9 y - 4 z = 4

Isolate

x

for

2 x + 3 y + 4 z = 3 : x = \frac{3 - 3 y - 4 z}{2}

Substitute

x = \frac{3 - 3 y - 4 z}{2}

[2 \cdot \frac{3 - 3 y - 4 z}{2} + 6 y + 8 z = 5 4 \cdot \frac{3 - 3 y - 4 z}{2} + 9 y - 4 z = 4]

Simplify

[3 y + 4 z + 3 = 5 3 y - 12 z + 6 = 4]

Isolate

y

for

3 y + 4 z + 3 = 5 : y = \frac{- 4 z + 2}{3}

Substitute

y = \frac{- 4 z + 2}{3}

[3 \cdot \frac{- 4 z + 2}{3} - 12 z + 6 = 4]

Simplify

[- 16 z + 8 = 4]

Isolate

z

for

- 16 z + 8 = 4 : z = \frac{1}{4}

For

y = \frac{- 4 z + 2}{3}

Substitute

z = \frac{1}{4}

y = \frac{- 4 \cdot \frac{1}{4} + 2}{3}

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

y = \frac{1}{3}

For

x = \frac{3 - 3 y - 4 z}{2}

Substitute

y = \frac{1}{3}, z = \frac{1}{4}

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

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

x = \frac{1}{2}

The solutions to the system of equations are:

x = \frac{1}{2}, y = \frac{1}{3}, z = \frac{1}{4}

x + 3 y = 3, 2 x - y = 1.8

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

x + 3 y = 1, 2 - 2 x - 4 y = 24

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

5 x + 4 y = 20, 8 x - 5 y = 15

What is 2x+3y+4z=3,2x+6y+8z=5,4x+9y-4z=4 ?
The solution to 2x+3y+4z=3,2x+6y+8z=5,4x+9y-4z=4 is x= 1/2 ,y= 1/3 ,z= 1/4