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

The solution to x-2y+3z=2,3x-y+4z=4,2x+y-2z=5 is x= 11/5 ,y=-7/5 ,z=-1

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

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

x = \frac{11}{5}, y = - \frac{7}{5}, z = - 1

Solution steps

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

Isolate

x

for

x - 2 y + 3 z = 2 : x = 2 + 2 y - 3 z

Substitute

x = 2 + 2 y - 3 z

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

Simplify

[5 y - 5 z + 6 = 4 5 y - 8 z + 4 = 5]

Isolate

y

for

5 y - 5 z + 6 = 4 : y = \frac{5 z - 2}{5}

Substitute

y = \frac{5 z - 2}{5}

[5 \cdot \frac{5 z - 2}{5} - 8 z + 4 = 5]

Simplify

[- 3 z + 2 = 5]

Isolate

z

for

- 3 z + 2 = 5 : z = - 1

For

y = \frac{5 z - 2}{5}

Substitute

z = - 1

y = \frac{5 ( - 1 ) - 2}{5}

\frac{5 ( - 1 ) - 2}{5} = - \frac{7}{5}

y = - \frac{7}{5}

For

x = 2 + 2 y - 3 z

Substitute

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

x = 2 + 2 (- \frac{7}{5}) - 3 (- 1)

2 + 2 (- \frac{7}{5}) - 3 (- 1) = \frac{11}{5}

x = \frac{11}{5}

The solutions to the system of equations are:

x = \frac{11}{5}, y = - \frac{7}{5}, z = - 1

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

3 x + 2 y = 6, 2 x + 3 y = 9

3 x - 2 y = 5, - 2 x + 3 y = 0

2 x - 7 y = 7, 3 x + y = 22

5 b = 5, a = 12

What is x-2y+3z=2,3x-y+4z=4,2x+y-2z=5 ?
The solution to x-2y+3z=2,3x-y+4z=4,2x+y-2z=5 is x= 11/5 ,y=-7/5 ,z=-1