20. $$ \left\{\begin{array}{l}-4 m+3 n-6=0 \ n=\frac{-1}{3} m-8\end{array} ight. $$

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20. $$ \left\{\begin{array}{l}-4 m+3 n-6=0 \ n=\frac{-1}{3} m-8\end{array}ight. $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ -4m+3n-6=0; n=\frac{-1}{3}m-8 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}-4m+3n-6=0\n=\frac{-1}{3}m-8\end{array}ight.$$
- step1: Calculate:
  $$\left\{ \begin{array}{l}-4m+3n-6=0\n=-\frac{1}{3}m-8\end{array}ight.$$
- step2: Substitute the value of $$n:$$
  $$-4m+3\left(-\frac{1}{3}m-8ight)-6=0$$
- step3: Simplify:
  $$-5m-30=0$$
- step4: Move the constant to the right side:
  $$-5m=0+30$$
- step5: Remove 0:
  $$-5m=30$$
- step6: Change the signs:
  $$5m=-30$$
- step7: Divide both sides:
  $$\frac{5m}{5}=\frac{-30}{5}$$
- step8: Divide the numbers:
  $$m=-6$$
- step9: Substitute the value of $$m:$$
  $$n=-\frac{1}{3}\left(-6ight)-8$$
- step10: Simplify:
  $$n=-6$$
- step11: Calculate:
  $$\left\{ \begin{array}{l}m=-6\n=-6\end{array}ight.$$
- step12: Check the solution:
  $$\left\{ \begin{array}{l}m=-6\n=-6\end{array}ight.$$
- step13: Rewrite:
  $$\left(m,night) = \left(-6,-6ight)$$
The solution to the system of equations is $$ m = -6 $$ and $$ n = -6 $$.
$$ m = -6 $$, $$ n = -6 $$

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