What is 2x+3y-z=7,-x+5y+2z=14,2x+y-3z=-3 ?

The solution to 2x+3y-z=7,-x+5y+2z=14,2x+y-3z=-3 is x=2,y=2,z=3

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2x+3y-z=7,-x+5y+2z=14,2x+y-3z=-3

2 x + 3 y - z = 7, - x + 5 y + 2 z = 14, 2 x + y - 3 z = - 3

x = 2, y = 2, z = 3

Solution steps

2 x + 3 y - z = 7 - x + 5 y + 2 z = 14 2 x + y - 3 z = - 3

Isolate

x

for

2 x + 3 y - z = 7 : x = \frac{7 - 3 y + z}{2}

Substitute

x = \frac{7 - 3 y + z}{2}

[- \frac{7 - 3 y + z}{2} + 5 y + 2 z = 14 2 \cdot \frac{7 - 3 y + z}{2} + y - 3 z = - 3]

Simplify

[\frac{13 y + 3 z - 7}{2} = 14 - 2 y - 2 z + 7 = - 3]

Isolate

y

for

\frac{13 y + 3 z - 7}{2} = 14 : y = \frac{- 3 z + 35}{13}

Substitute

y = \frac{- 3 z + 35}{13}

[- 2 \cdot \frac{- 3 z + 35}{13} - 2 z + 7 = - 3]

Simplify

[\frac{- 20 z - 70}{13} + 7 = - 3]

Isolate

z

for

\frac{- 20 z - 70}{13} + 7 = - 3 : z = 3

For

y = \frac{- 3 z + 35}{13}

Substitute

z = 3

y = \frac{- 3 \cdot 3 + 35}{13}

\frac{- 3 \cdot 3 + 35}{13} = 2

y = 2

For

x = \frac{7 - 3 y + z}{2}

Substitute

y = 2, z = 3

x = \frac{7 - 3 \cdot 2 + 3}{2}

\frac{7 - 3 \cdot 2 + 3}{2} = 2

x = 2

The solutions to the system of equations are:

x = 2, y = 2, z = 3

x - 2 y = 4, x + y = 17

3 x - y = 2, x + 2 y = 10

3 x - 4 y = 11, 5 x - 3 y = 33

a + 4 b = 9, 5 a + 4 b = 29

y = 0, y = - 1

What is 2x+3y-z=7,-x+5y+2z=14,2x+y-3z=-3 ?
The solution to 2x+3y-z=7,-x+5y+2z=14,2x+y-3z=-3 is x=2,y=2,z=3