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

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

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x-3y+z=2,4x-4y+z=7,2x+y-3z=-4

x - 3 y + z = 2, 4 x - 4 y + z = 7, 2 x + y - 3 z = - 4

x = 2, y = 1, z = 3

Solution steps

x - 3 y + z = 2 4 x - 4 y + z = 7 2 x + y - 3 z = - 4

Isolate

x

for

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

Substitute

x = 2 + 3 y - z

[4 (2 + 3 y - z) - 4 y + z = 7 2 (2 + 3 y - z) + y - 3 z = - 4]

Simplify

[8 y - 3 z + 8 = 7 7 y - 5 z + 4 = - 4]

Isolate

y

for

8 y - 3 z + 8 = 7 : y = \frac{3 z - 1}{8}

Substitute

y = \frac{3 z - 1}{8}

[7 \cdot \frac{3 z - 1}{8} - 5 z + 4 = - 4]

Simplify

[\frac{- 19 z - 7}{8} + 4 = - 4]

Isolate

z

for

\frac{- 19 z - 7}{8} + 4 = - 4 : z = 3

For

y = \frac{3 z - 1}{8}

Substitute

z = 3

y = \frac{3 \cdot 3 - 1}{8}

Simplify

y = 1

For

x = 2 + 3 y - z

Substitute

y = 1, z = 3

x = 2 + 3 \cdot 1 - 3

Simplify

x = 2

The solutions to the system of equations are:

x = 2, y = 1, z = 3

3 x + 5 y = 11, 2 x - y = 16

x - 2 y = 4, x - 2 y = 0, x + y = 4, x + y = 1

4 x + y = 3, 4 x + 4 y = 16

x = 5 y + 8, - 7 x + 8 y = 25

5 x + 6 y = 12, 3 x + 5 y = 21

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