What is x+y+z=18,4x+2y+z=36,6x+5y+4z=36 ?

The solution to x+y+z=18,4x+2y+z=36,6x+5y+4z=36 is x=54,y=-144,z=108

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x+y+z=18,4x+2y+z=36,6x+5y+4z=36

x + y + z = 18, 4 x + 2 y + z = 36, 6 x + 5 y + 4 z = 36

x = 54, y = - 144, z = 108

Solution steps

x + y + z = 18 4 x + 2 y + z = 36 6 x + 5 y + 4 z = 36

Isolate

x

for

x + y + z = 18 : x = 18 - y - z

Substitute

x = 18 - y - z

[4 (18 - y - z) + 2 y + z = 36 6 (18 - y - z) + 5 y + 4 z = 36]

Simplify

[- 2 y - 3 z + 72 = 36 - y - 2 z + 108 = 36]

Isolate

y

for

- 2 y - 3 z + 72 = 36 : y = - \frac{3 z - 36}{2}

Substitute

y = - \frac{3 z - 36}{2}

[- (- \frac{3 z - 36}{2}) - 2 z + 108 = 36]

Simplify

[\frac{- z - 36}{2} + 108 = 36]

Isolate

z

for

\frac{- z - 36}{2} + 108 = 36 : z = 108

For

y = - \frac{3 z - 36}{2}

Substitute

z = 108

y = - \frac{3 \cdot 108 - 36}{2}

- \frac{3 \cdot 108 - 36}{2} = - 144

y = - 144

For

x = 18 - y - z

Substitute

y = - 144, z = 108

x = 18 - (- 144) - 108

Simplify

x = 54

The solutions to the system of equations are:

x = 54, y = - 144, z = 108

2 x - 3 y = 4, x + 5 y = 15

a + b = c, c = 3 d

x + 2 y = - 12, 3 x - y = - 1

\frac{2}{x} + \frac{3}{y} = 6, \frac{4}{x} + \frac{5}{y} = 9

6 x + 4 y = 3, 5 x - 102 y = 2

What is x+y+z=18,4x+2y+z=36,6x+5y+4z=36 ?
The solution to x+y+z=18,4x+2y+z=36,6x+5y+4z=36 is x=54,y=-144,z=108