Question

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

Answer 1

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