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

The solution to x+2y+z=2,-y+z=-3 is x=-3z-4,y=3+z

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

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

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

Solution steps

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

Isolate

y

for

- y + z = - 3 : y = 3 + z

Substitute

y = 3 + z

[x + 2 (3 + z) + z = 2]

Simplify

[x + 6 + 3 z = 2]

Isolate

x

for

x + 6 + 3 z = 2 : x = - 3 z - 4

Expressing

y

in terms of

z

y = 3 + z

The solutions to the system of equations are:

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

\frac{1}{15} b = - \frac{7}{6}, a = 1

x - 5 y = 31, 3 x + 5 y = - 7

x - y = 1, x - 3 y = - 3

x + y = 5, 2 x - 3 y = 1

12 x - 7 y = 15, 3 x + 6 y = 4