How do you solve the system of equations #3m - 2n = - 3# and #9m - 7n= - 12#?

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Answer 1 · 2016-11-22T21:07:39

#n = 3# and #m = 1#

Step 1) Solve the first equation for #m#:

#3m - 2n + 2n = 2n - 3#

#3m = 2n - 3#

#(3m)/3 = (2n - 3)/3#

#m = (2n)/3 - 3/3#

#m = (2n)/3 - 1#

Step 2) Substitute #(2n)/3 - 1# for #m# in the second equation and solve for #n#:

#9((2n)/3 - 1) - 7n = -12#

#(18n/3) - 9 - 7n = -12#

#6n - 9 - 7n + 9 = -12 + 9#

#-1n = -3#

#(-1n)/-1 = (-3)/(-1)#

#n = 3#

Step 3) Substitute #3# for #n# in the solution for the first equation and solve for #m#:

#m = (2 * 3)/3 - 1#

#m = 2 - 1#

#m = 1#