What is 2x-y+2z=6,3x+2y-z=4,4x+3y-3z=1 ?

The solution to 2x-y+2z=6,3x+2y-z=4,4x+3y-3z=1 is x=1,y=2,z=3

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2x-y+2z=6,3x+2y-z=4,4x+3y-3z=1

2 x - y + 2 z = 6, 3 x + 2 y - z = 4, 4 x + 3 y - 3 z = 1

x = 1, y = 2, z = 3

Solution steps

2 x - y + 2 z = 6 3 x + 2 y - z = 4 4 x + 3 y - 3 z = 1

Isolate

x

for

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

Substitute

x = \frac{6 + y - 2 z}{2}

[3 \cdot \frac{6 + y - 2 z}{2} + 2 y - z = 4 4 \cdot \frac{6 + y - 2 z}{2} + 3 y - 3 z = 1]

Simplify

[\frac{7 y - 8 z + 18}{2} = 4 5 y - 7 z + 12 = 1]

Isolate

y

for

\frac{7 y - 8 z + 18}{2} = 4 : y = \frac{8 z - 10}{7}

Substitute

y = \frac{8 z - 10}{7}

[5 \cdot \frac{8 z - 10}{7} - 7 z + 12 = 1]

Simplify

[\frac{- 9 z - 50}{7} + 12 = 1]

Isolate

z

for

\frac{- 9 z - 50}{7} + 12 = 1 : z = 3

For

y = \frac{8 z - 10}{7}

Substitute

z = 3

y = \frac{8 \cdot 3 - 10}{7}

\frac{8 \cdot 3 - 10}{7} = 2

y = 2

For

x = \frac{6 + y - 2 z}{2}

Substitute

y = 2, z = 3

x = \frac{6 + 2 - 2 \cdot 3}{2}

Simplify

x = 1

The solutions to the system of equations are:

x = 1, y = 2, z = 3

12 x - 8 y = 4, 10 x - 20 y = - 2

5 = 2 a + b, 2 = 3 a + b

8 x + 5 y = - 28, 9 x + 6 y = - 33

2 x - y = 0, x - 2 y = 6

3 x + 2 y = - 25, - 2 x - y = 10

What is 2x-y+2z=6,3x+2y-z=4,4x+3y-3z=1 ?
The solution to 2x-y+2z=6,3x+2y-z=4,4x+3y-3z=1 is x=1,y=2,z=3