What is 4n-2m-3r=1,m+3n+5r=-4,3m-5n+r=0 ?

The solution to 4n-2m-3r=1,m+3n+5r=-4,3m-5n+r=0 is r=-11/21 ,n=-1/3 ,m=-8/21

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4n-2m-3r=1,m+3n+5r=-4,3m-5n+r=0

4 n - 2 m - 3 r = 1, m + 3 n + 5 r = - 4, 3 m - 5 n + r = 0

r = - \frac{11}{21}, n = - \frac{1}{3}, m = - \frac{8}{21}

Solution steps

4 n - 2 m - 3 r = 1 m + 3 n + 5 r = - 4 3 m - 5 n + r = 0

Isolate

n

for

4 n - 2 m - 3 r = 1 : n = \frac{1 + 2 m + 3 r}{4}

Substitute

n = \frac{1 + 2 m + 3 r}{4}

[m + 3 \cdot \frac{1 + 2 m + 3 r}{4} + 5 r = - 4 3 m - 5 \cdot \frac{1 + 2 m + 3 r}{4} + r = 0]

Simplify

[\frac{29 r + 10 m + 3}{4} = - 4 \frac{- 11 r + 2 m - 5}{4} = 0]

Isolate

r

for

\frac{29 r + 10 m + 3}{4} = - 4 : r = \frac{- 10 m - 19}{29}

Substitute

r = \frac{- 10 m - 19}{29}

[\frac{- 11 \cdot \frac{- 10 m - 19}{29} + 2 m - 5}{4} = 0]

Simplify

[\frac{2 ( 21 m + 8 )}{29} = 0]

Isolate

m

for

\frac{2 ( 21 m + 8 )}{29} = 0 : m = - \frac{8}{21}

For

r = \frac{- 10 m - 19}{29}

Substitute

m = - \frac{8}{21}

r = \frac{- 10 ( - \frac{8}{21} ) - 19}{29}

\frac{- 10 ( - \frac{8}{21} ) - 19}{29} = - \frac{11}{21}

r = - \frac{11}{21}

For

n = \frac{1 + 2 m + 3 r}{4}

Substitute

r = - \frac{11}{21}, m = - \frac{8}{21}

n = \frac{1 + 2 ( - \frac{8}{21} ) + 3 ( - \frac{11}{21} )}{4}

\frac{1 + 2 ( - \frac{8}{21} ) + 3 ( - \frac{11}{21} )}{4} = - \frac{1}{3}

n = - \frac{1}{3}

The solutions to the system of equations are:

r = - \frac{11}{21}, n = - \frac{1}{3}, m = - \frac{8}{21}

3 x - 4 y = 6, 4 x + 5 y = 2

5 x + 3 y = 1, \frac{3}{4} \cdot x - y = 2

3 x - y = 5, 4 x - 3 y = - 1

x + y = 4, 1 x = 5 + y

5 x + y = - 19, 7 x - y = - 16

What is 4n-2m-3r=1,m+3n+5r=-4,3m-5n+r=0 ?
The solution to 4n-2m-3r=1,m+3n+5r=-4,3m-5n+r=0 is r=-11/21 ,n=-1/3 ,m=-8/21