What is 5x-6y-z=12,4x-3y+4z=15 ?

The solution to 5x-6y-z=12,4x-3y+4z=15 is x=3(-z+2),y=(-8z+9)/3

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5x-6y-z=12,4x-3y+4z=15

5 x - 6 y - z = 12, 4 x - 3 y + 4 z = 15

x = 3 (- z + 2), y = \frac{- 8 z + 9}{3}

Solution steps

[5 x - 6 y - z = 12 4 x - 3 y + 4 z = 15]

Isolate

x

for

5 x - 6 y - z = 12 : x = \frac{12 + 6 y + z}{5}

Substitute

x = \frac{12 + 6 y + z}{5}

[4 \cdot \frac{12 + 6 y + z}{5} - 3 y + 4 z = 15]

Simplify

[\frac{9 y + 24 z + 48}{5} = 15]

Isolate

y

for

\frac{9 y + 24 z + 48}{5} = 15 : y = \frac{- 8 z + 9}{3}

For

x = \frac{12 + 6 y + z}{5}

Expressing

x

in terms of

z

x = \frac{12 + 6 \cdot \frac{- 8 z + 9}{3} + z}{5}

Simplify

\frac{12 + 6 \cdot \frac{- 8 z + 9}{3} + z}{5} : 3 (- z + 2)

x = 3 (- z + 2)

The solutions to the system of equations are:

x = 3 (- z + 2), y = \frac{- 8 z + 9}{3}

3 x - 5 y = 4, 9 x - 2 y = 7

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

4 x + 6 y = 24, 2 x + 3 y = 6

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

x - 3 y + 2 z = - 3, 5 x + 6 y - z = 13, 4 x - y + 3 z = 8

What is 5x-6y-z=12,4x-3y+4z=15 ?
The solution to 5x-6y-z=12,4x-3y+4z=15 is x=3(-z+2),y=(-8z+9)/3