What is (4)5m-3n=19,m^6n=-7 ?

The solution to (4)5m-3n=19,m^6n=-7 is

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(4)5m-3n=19,m^6n=-7

(4) 5 m - 3 n = 19, m^{6} n = - 7

(m = - 0.90916 \dots, n = - 12.39446 \dots)

Solution steps

[(4) \cdot 5 m - 3 n = 19 m^{6} n = - 7]

Isolate

n

for

(4) 5 m - 3 n = 19 : n = - \frac{19 - 20 m}{3}

Plug the solutions

n = - \frac{19 - 20 m}{3}

into

m^{6} n = - 7

For

m^{6} n = - 7

, subsitute

n

with

- \frac{19 - 20 m}{3} : m \approx - 0.90916 \dots

Plug the solutions

m = - 0.90916 \dots

into

(4) 5 m - 3 n = 19

For

(4) 5 m - 3 n = 19

, subsitute

m

with

- 0.90916 \dots : n = - 12.39446 \dots

Verify solutions by plugging them into the original equations

Therefore, the final solution for

(4) 5 m - 3 n = 19, m^{6} n = - 7

(m = - 0.90916 \dots, n = - 12.39446 \dots)

x + y = 3, x + 6 y = 9

x + y = 7, 6 x + 5 y = 9

+ 3 a \cdot x_{2} = 4 - 91, x_{1} = 2

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

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