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

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

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

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

x = 1, y = 1, z = 1

Solution steps

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

Isolate

x

for

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

Substitute

x = \frac{4 - y - z}{2}

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

Simplify

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

Isolate

y

for

\frac{- 7 y - 5 z + 4}{2} = - 4 : y = - \frac{5 z - 12}{7}

Substitute

y = - \frac{5 z - 12}{7}

[- (- \frac{5 z - 12}{7}) - 5 z + 8 = 2]

Simplify

[\frac{- 30 z - 12}{7} + 8 = 2]

Isolate

z

for

\frac{- 30 z - 12}{7} + 8 = 2 : z = 1

For

y = - \frac{5 z - 12}{7}

Substitute

z = 1

y = - \frac{5 \cdot 1 - 12}{7}

- \frac{5 \cdot 1 - 12}{7} = 1

y = 1

For

x = \frac{4 - y - z}{2}

Substitute

y = 1, z = 1

x = \frac{4 - 1 - 1}{2}

Simplify

x = 1

The solutions to the system of equations are:

x = 1, y = 1, z = 1

7 m + 7 n = 11, 27 m + 6 n = 108

7 x + 10 y = 3, 6 y = 2 x + 9

5 x + 6 y = 20, 3 x + 8 y = 34

x + y - z + t = 6, y + z = 1, z + 2 t = 6, 2 t = 8

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

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