What is x-y=z,y=4z,x+y=81 ?

The solution to x-y=z,y=4z,x+y=81 is x=45,y=36,z=9

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x-y=z,y=4z,x+y=81

x - y = z, y = 4 z, x + y = 81

x = 45, y = 36, z = 9

Solution steps

x - y = z y = 4 z x + y = 81

Substitute

y = 4 z

[x + 4 z = 81 x - 4 z = z]

Isolate

x

for

x + 4 z = 81 : x = 81 - 4 z

Substitute

x = 81 - 4 z

[81 - 4 z - 4 z = z]

Simplify

[81 - 8 z = z]

Isolate

z

for

81 - 8 z = z : z = 9

For

x = 81 - 4 z

Substitute

z = 9

x = 81 - 4 \cdot 9

Simplify

x = 45

For

y = 4 z

Substitute

x = 45, z = 9

y = 4 \cdot 9

Simplify

y = 36

The solutions to the system of equations are:

x = 45, y = 36, z = 9

a + b = 3, b + c = 4, c + a = 5

2 x - 3 y = - 16, 5 x + 3 y = 2

9 x - 4 y = 23, 2 x - y = 12

10 x + 8 y + z = 20, 0 x + y + z = 100

3 x + 4 y + 10 = 0, x - y = 2