What is x+y+z=11,x-y+3z=13,2x+2y-z=7 ?

The solution to x+y+z=11,x-y+3z=13,2x+2y-z=7 is x=2,y=4,z=5

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x+y+z=11,x-y+3z=13,2x+2y-z=7

x + y + z = 11, x - y + 3 z = 13, 2 x + 2 y - z = 7

x = 2, y = 4, z = 5

Solution steps

x + y + z = 11 x - y + 3 z = 13 2 x + 2 y - z = 7

Isolate

x

for

x + y + z = 11 : x = 11 - y - z

Substitute

x = 11 - y - z

[11 - y - z - y + 3 z = 13 2 (11 - y - z) + 2 y - z = 7]

Simplify

[- 2 y + 2 z + 11 = 13 - 3 z + 22 = 7]

Isolate

z

for

- 3 z + 22 = 7 : z = 5

Substitute

z = 5

[- 2 y + 2 \cdot 5 + 11 = 13]

Simplify

[- 2 y + 21 = 13]

Isolate

y

for

- 2 y + 21 = 13 : y = 4

For

x = 11 - y - z

Substitute

y = 4, z = 5

x = 11 - 4 - 5

Simplify

x = 2

The solutions to the system of equations are:

x = 2, y = 4, z = 5

11 x - 13 y = 53, 7 x + 9 y = - 139

4 x + 3 y = 18, 5 x + 6 y = 27

\frac{x}{2} + y = 0, x - \frac{y}{3} = \frac{1}{2}

7 x + 3 y = 46, 12 x - 5 y = 18

a = 4, b = 2

What is x+y+z=11,x-y+3z=13,2x+2y-z=7 ?
The solution to x+y+z=11,x-y+3z=13,2x+2y-z=7 is x=2,y=4,z=5