Solve {l}{8a+4*5n+6m=2320}{a+n+m=405}{2n=a}

$$\left\{ \begin{array} { l } { 8 a + 4 \cdot 5 n + 6 m = 2320 } \\ { a + n + m = 405 } \\ { 2 n = a } \end{array} \right.$$

Solve for a, n, m

$$a = -\frac{110}{9} = -12\frac{2}{9} \approx -12.222222222$$

$$n = -\frac{55}{9} = -6\frac{1}{9} \approx -6.111111111$$

$$m = \frac{1270}{3} = 423\frac{1}{3} \approx 423.333333333$$

Short Steps Using Substitution

Reorder the equations.

$$2n=a a+n+m=405 8a+4\times 5n+6m=2320$$

Solve 2n=a for a.

$$a=2n$$

Substitute 2n for a in the second and third equation.

$$2n+n+m=405 8\times 2n+4\times 5n+6m=2320$$

Solve these equations for n and m respectively.

$$n=-\frac{1}{3}m+135 m=\frac{1160}{3}-6n$$

Substitute -\frac{1}{3}m+135 for n in the equation m=\frac{1160}{3}-6n.

$$m=\frac{1160}{3}-6\left(-\frac{1}{3}m+135\right)$$

Solve m=\frac{1160}{3}-6\left(-\frac{1}{3}m+135\right) for m.

$$m=\frac{1270}{3}$$

Substitute \frac{1270}{3} for m in the equation n=-\frac{1}{3}m+135.

$$n=-\frac{1}{3}\times \frac{1270}{3}+135$$

Calculate n from n=-\frac{1}{3}\times \frac{1270}{3}+135.

$$n=-\frac{55}{9}$$

Substitute -\frac{55}{9} for n in the equation a=2n.

$$a=2\left(-\frac{55}{9}\right)$$

Calculate a from a=2\left(-\frac{55}{9}\right).

$$a=-\frac{110}{9}$$

The system is now solved.

$$a=-\frac{110}{9} n=-\frac{55}{9} m=\frac{1270}{3}$$