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

The solution to x+y+z=1,6x-y+z=0,-9y+9z=-27 is x= 1/2 ,y= 7/4 ,z=-5/4

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

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

x = \frac{1}{2}, y = \frac{7}{4}, z = - \frac{5}{4}

Solution steps

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

Isolate

y

for

- 9 y + 9 z = - 27 : y = z + 3

Substitute

y = z + 3

[x + z + 3 + z = 1 6 x - (z + 3) + z = 0]

Simplify

[2 z + x + 3 = 1 6 x - 3 = 0]

Isolate

x

for

6 x - 3 = 0 : x = \frac{1}{2}

Substitute

x = \frac{1}{2}

[2 z + \frac{1}{2} + 3 = 1]

Simplify

[2 z + \frac{7}{2} = 1]

Isolate

z

for

2 z + \frac{7}{2} = 1 : z = - \frac{5}{4}

For

y = z + 3

Substitute

x = \frac{1}{2}, z = - \frac{5}{4}

y = - \frac{5}{4} + 3

- \frac{5}{4} + 3 = \frac{7}{4}

y = \frac{7}{4}

The solutions to the system of equations are:

x = \frac{1}{2}, y = \frac{7}{4}, z = - \frac{5}{4}

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

- 5 x + 6 y = 7, 4 x + 3 y = 10

x + 3 y = 6, 5 x - 2 y = 12

3 x - 5 y = 1, 2 x + 3 y = 7

4 x - 6 y = 5, 3 x + 2 y = - 14

What is x+y+z=1,6x-y+z=0,-9y+9z=-27 ?
The solution to x+y+z=1,6x-y+z=0,-9y+9z=-27 is x= 1/2 ,y= 7/4 ,z=-5/4