What is 2x+3y+4z=7,4y=2+5z,3z-2x+6=0 ?

The solution to 2x+3y+4z=7,4y=2+5z,3z-2x+6=0 is x= 126/43 ,y= 19/43 ,z=-2/43

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2x+3y+4z=7,4y=2+5z,3z-2x+6=0

2 x + 3 y + 4 z = 7, 4 y = 2 + 5 z, 3 z - 2 x + 6 = 0

x = \frac{126}{43}, y = \frac{19}{43}, z = - \frac{2}{43}

Solution steps

2 x + 3 y + 4 z = 7 4 y = 2 + 5 z 3 z - 2 x + 6 = 0

Isolate

y

for

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

Substitute

y = \frac{2 + 5 z}{4}

[3 z - 2 x + 6 = 0 2 x + 3 \cdot \frac{2 + 5 z}{4} + 4 z = 7]

Simplify

[3 z - 2 x + 6 = 0 2 x + \frac{6 + 31 z}{4} = 7]

Isolate

z

for

3 z - 2 x + 6 = 0 : z = \frac{2 x - 6}{3}

Substitute

z = \frac{2 x - 6}{3}

[2 x + \frac{6 + 31 \cdot \frac{2 x - 6}{3}}{4} = 7]

Simplify

[\frac{43 x - 84}{6} = 7]

Isolate

x

for

\frac{43 x - 84}{6} = 7 : x = \frac{126}{43}

For

z = \frac{2 x - 6}{3}

Substitute

x = \frac{126}{43}

z = \frac{2 \cdot \frac{126}{43} - 6}{3}

\frac{2 \cdot \frac{126}{43} - 6}{3} = - \frac{2}{43}

z = - \frac{2}{43}

For

y = \frac{2 + 5 z}{4}

Substitute

x = \frac{126}{43}, z = - \frac{2}{43}

y = \frac{2 + 5 ( - \frac{2}{43} )}{4}

\frac{2 + 5 ( - \frac{2}{43} )}{4} = \frac{19}{43}

y = \frac{19}{43}

The solutions to the system of equations are:

x = \frac{126}{43}, y = \frac{19}{43}, z = - \frac{2}{43}

x + 3 y = 1, 4 x - y = 17

x + y = 14, x - y = 4

2 x - y = 2, 4 x - 4 y = 6

x + y + z = 1, 6 x - y + z = 0, - 9 y + 9 z = - 27

9 a + 5 b = 15, 3 a + 2 b = - 6

What is 2x+3y+4z=7,4y=2+5z,3z-2x+6=0 ?
The solution to 2x+3y+4z=7,4y=2+5z,3z-2x+6=0 is x= 126/43 ,y= 19/43 ,z=-2/43