How do you solve #m+2n=1# and #5m+3n= -23#?

1 Answer
May 11, 2018

Answer:

n = -4, m = 9

Explanation:

#m + 2n = 1#
#5m + 3n = -23#

This is a system of equations, and the best way to solve this one is through substitution. Basically, we're going to isolate for 1 variable and plug it into the second question to get both variables.

#m + 2n = 1#

Let's find m. Subtract 2n from both sides. You should get:

#m = -2n + 1#

Now that we know what #m# is, we can plug it into our second equation:

#5(-2n + 1) + 3n = -23#

Distribute.

#-10n + 5 + 3n = -23#

Combine like terms.

#7n + 5 = -23#

Subtract 5 from both sides.

#7n = -28#

Divide by 7 to isolate for n.

#n = -4#

Now, plug this back into the first equation:

#m = -2n + 1#
#m = -2(-4) + 1#

Multiply.

#m# = 8 + 1
#m# = 9

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-with-substitution/v/the-substitution-method