What is x+y+2z=1,2x+2y+3z=2 ?

The solution to x+y+2z=1,2x+2y+3z=2 is x=-y+1,z=0

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x+y+2z=1,2x+2y+3z=2

x + y + 2 z = 1, 2 x + 2 y + 3 z = 2

x = - y + 1, z = 0

Solution steps

[x + y + 2 z = 1 2 x + 2 y + 3 z = 2]

Isolate

x

for

x + y + 2 z = 1 : x = 1 - y - 2 z

Substitute

x = 1 - y - 2 z

[2 (1 - y - 2 z) + 2 y + 3 z = 2]

Simplify

[- z + 2 = 2]

Isolate

z

for

- z + 2 = 2 : z = 0

For

x = 1 - y - 2 z

Expressing

x

in terms of

y

x = 1 - y - 2 \cdot 0

Simplify

1 - y - 2 \cdot 0 : - y + 1

x = - y + 1

The solutions to the system of equations are:

x = - y + 1, z = 0

5 x - 3 y = 60, - 4 x + 9 y = 17

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

x + 5 y = 9, 2 x + 3 y = 11

3 x + y = 7, x - y = 1

g (0) = 1, g (n) = g (n - 1) - g (n - 2) g (4)