What is x-y+4z=5,2x+z=0,x+3y+z=-15 ?

The solution to x-y+4z=5,2x+z=0,x+3y+z=-15 is x=0,y=-5,z=0

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x-y+4z=5,2x+z=0,x+3y+z=-15

x - y + 4 z = 5, 2 x + z = 0, x + 3 y + z = - 15

x = 0, y = - 5, z = 0

Solution steps

x - y + 4 z = 5 2 x + z = 0 x + 3 y + z = - 15

Isolate

x

for

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

Substitute

x = - \frac{z}{2}

[- \frac{z}{2} - y + 4 z = 5 - \frac{z}{2} + 3 y + z = - 15]

Simplify

[- y + \frac{7 z}{2} = 5 3 y + \frac{z}{2} = - 15]

Isolate

y

for

- y + \frac{7 z}{2} = 5 : y = - \frac{10 - 7 z}{2}

Substitute

y = - \frac{10 - 7 z}{2}

[3 (- \frac{10 - 7 z}{2}) + \frac{z}{2} = - 15]

Simplify

[- 15 + 11 z = - 15]

Isolate

z

for

- 15 + 11 z = - 15 : z = 0

For

y = - \frac{10 - 7 z}{2}

Substitute

z = 0

y = - \frac{10 - 7 \cdot 0}{2}

- \frac{10 - 7 \cdot 0}{2} = - 5

y = - 5

For

x = - \frac{z}{2}

Substitute

y = - 5, z = 0

x = - \frac{0}{2}

- \frac{0}{2} = 0

x = 0

The solutions to the system of equations are:

x = 0, y = - 5, z = 0

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

55 x + 52 y = 21, 752 x + 55 y = 217

x - 3 y = - 2 x + 9, y = 4

- 3 x + 3 y = 1, 7 - 6 x + 6 y = - 5

5 x + 3 y = 16, 2 x + 3 y = 10

What is x-y+4z=5,2x+z=0,x+3y+z=-15 ?
The solution to x-y+4z=5,2x+z=0,x+3y+z=-15 is x=0,y=-5,z=0