What is 2x-y+3z=1,3x+2y-z=5 ?

The solution to 2x-y+3z=1,3x+2y-z=5 is x=(-5z+7)/7 ,y=(11z+7)/7

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

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

x = \frac{- 5 z + 7}{7}, y = \frac{11 z + 7}{7}

Solution steps

[2 x - y + 3 z = 1 3 x + 2 y - z = 5]

Isolate

x

for

2 x - y + 3 z = 1 : x = \frac{1 + y - 3 z}{2}

Substitute

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

[3 \cdot \frac{1 + y - 3 z}{2} + 2 y - z = 5]

Simplify

[\frac{7 y - 11 z + 3}{2} = 5]

Isolate

y

for

\frac{7 y - 11 z + 3}{2} = 5 : y = \frac{11 z + 7}{7}

For

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

Expressing

x

in terms of

z

x = \frac{1 + \frac{11 z + 7}{7} - 3 z}{2}

Simplify

\frac{1 + \frac{11 z + 7}{7} - 3 z}{2} : \frac{- 5 z + 7}{7}

x = \frac{- 5 z + 7}{7}

The solutions to the system of equations are:

x = \frac{- 5 z + 7}{7}, y = \frac{11 z + 7}{7}

x + 5 y = 15, 2 x - 3 y = 1

\frac{x}{2} - \frac{y}{5} = 4, \frac{x}{7} + \frac{y}{15} = 3

8 x - 2 y = 7, 2 x + 3 y = 5

x + y = 16, 2 x - y = 23

(4) 3 x - y - 2 = 0, 2 x + y = 8

What is 2x-y+3z=1,3x+2y-z=5 ?
The solution to 2x-y+3z=1,3x+2y-z=5 is x=(-5z+7)/7 ,y=(11z+7)/7