What is x+y+3z=10,x-y-z=-2,2x+3y+4z=4 ?

The solution to x+y+3z=10,x-y-z=-2,2x+3y+4z=4 is x=-3/2 ,y=-5,z= 11/2

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x+y+3z=10,x-y-z=-2,2x+3y+4z=4

x + y + 3 z = 10, x - y - z = - 2, 2 x + 3 y + 4 z = 4

x = - \frac{3}{2}, y = - 5, z = \frac{11}{2}

Solution steps

x + y + 3 z = 10 x - y - z = - 2 2 x + 3 y + 4 z = 4

Isolate

x

for

x + y + 3 z = 10 : x = 10 - y - 3 z

Substitute

x = 10 - y - 3 z

[10 - y - 3 z - y - z = - 2 2 (10 - y - 3 z) + 3 y + 4 z = 4]

Simplify

[- 2 y - 4 z + 10 = - 2 y - 2 z + 20 = 4]

Isolate

y

for

- 2 y - 4 z + 10 = - 2 : y = - 2 (z - 3)

Substitute

y = - 2 (z - 3)

[- 2 (z - 3) - 2 z + 20 = 4]

Simplify

[- 4 z + 26 = 4]

Isolate

z

for

- 4 z + 26 = 4 : z = \frac{11}{2}

For

y = - 2 (z - 3)

Substitute

z = \frac{11}{2}

y = - 2 (\frac{11}{2} - 3)

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

y = - 5

For

x = 10 - y - 3 z

Substitute

y = - 5, z = \frac{11}{2}

x = 10 - (- 5) - 3 \cdot \frac{11}{2}

10 - (- 5) - 3 \cdot \frac{11}{2} = - \frac{3}{2}

x = - \frac{3}{2}

The solutions to the system of equations are:

x = - \frac{3}{2}, y = - 5, z = \frac{11}{2}

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

3 x - \frac{2}{y} = 5, x + \frac{4}{y} = 4

x - y - 2 z = 0, - 2 x - 6 z = 1, - x + 2 y + z = 1

12 x + 16 y = 18, 14 x + 18 y = 20

x - y = 6, x + y = - 7

What is x+y+3z=10,x-y-z=-2,2x+3y+4z=4 ?
The solution to x+y+3z=10,x-y-z=-2,2x+3y+4z=4 is x=-3/2 ,y=-5,z= 11/2