# How do you solve #6m + n = 21# and #m - 8n = 28# using substitution?

##### 1 Answer

#### Explanation:

Take the second equation:

#m - 8n = 28#

If we add

#m = 8n + 28#

Now we have two equivalent expressions:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, look back at the first equation:

#6m + n = 21#

To solve by **substitution**, we need to replace (or **substitute**) one equivalent expression for the other so that we can solve this equation. Let's use the expressions from earlier:

#6color(red)m + n = 21#

Remember that *this*:

#6(color(blue)(8n + 28)) + n = 21#

Now, we can use simple algebra to solve for

#6(8n+28) + n = 21#

#6*8n + 6*28 + n = 21#

#48n + 168 + n = 21#

#49n + 168 = 21#

#49n = -147#

#n = -3#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Finally, let's plug

#6m + n = 21#

Remember from above that

#6m + color(orange)n = 21#

#6m + color(limegreen)((-3)) = 21#

#6m - 3 = 21#

#6m = 24#

#m = 4#

So now we have both parts of our solution! Here's the final solution:

#n = -3, " "m = 4#

*Final Answer*