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

1 Answer
Sep 7, 2015

Answer:

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

Explanation:

Your system of equations looks like this

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

You can solve this by substituting #2m# from the first equation into the second equation and solving for #n#, or by multplying the first equation by #(-1)#, adding the resulting equation to the second equation, and then solving for #n#.

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 #m# is equal to

#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, #m = 7# and #n = 4#.