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

1 Answer
John D.
Mar 22, 2018

n=−3, m=4

Explanation:

Take the second equation:

m−8n=28

If we add 8n to both sides, we get:

m=8n+28

Now we have two equivalent expressions: m and 8n+28.

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

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:

6m+n=21

Remember that m=8n+28, so we can do this:

6(8n+28)+n=21

Now, we can use simple algebra to solve for n.

6(8n+28)+n=21

6⋅8n+6⋅28+n=21

48n+168+n=21

49n+168=21

49n=−147

n=−3

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Finally, let's plug n back into one of the equations and solve for m to finish the problem. I'm using equation 1 to solve for m, but either one will work just fine.

6m+n=21

Remember from above that n=−3

6m+n=21

6m+(−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

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