# How do you solve 2m-5n=-6 and 2m-7n=-14?

##### 1 Answer

#### Explanation:

Your system of equations looks like this

#{(2m - 5n = -6), (2m - 7n = -14) :}#

You can solve this by substituting

Here's how that first method would look.

#2m = - 6 + 5n#

#(-6 + 5m) - 7n = -14#

#5m - 7n = -14 + 6#

#-2n = -8 implies n = ((-8))/((-2)) = 4#

This means that

#2m = -6 + 5 * (4)#

#m = 14/2 = 7#

The solution set will thus be

#{(n=4), (m = 7) :}#

Now try the second method.

#{(2m - 5n = -6 | (-1)), (2m - 7n = -14) :}#

#{(-2m + 5n = 6), (2m - 7n = -14) :}#

#stackrel("-------------------------------------------")#

#-color(red)(cancel(color(black)(2m))) + 5n + color(red)(cancel(color(black)(2m))) - 7n = 6 + (-14)#

#-2n = -8 implies n = 4#

Once again,