How do you solve this system of equations: #2m - n = 13 and 3m - 8n = 13#?

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Answer 1 · 2017-10-23T16:35:15

See a solution process below:

Step 1: Solve the first equation for #n#:

#2m - n = 13#

#-color(red)(2m) + 2m - n = -color(red)(2m) + 13#

#0 - n = -2m + 13#

#-n = -2m + 13#

#color(red)(-1) xx -n = color(red)(-1)(-2m + 13)#

#n = (color(red)(-1) xx -2m) + (color(red)(-1) xx 13)#

#n = 2m + (-13)#

#n = 2m - 13#

Step 2: Substitute #(2m - 13)# for #n# in the second equation and solve for #m#:

#3m - 8n = 13# becomes:

#3m - 8(2m - 13) = 13#

#3m - (8 xx 2m) + (8 xx 13) = 13#

#3m - 16m + 104 = 13#

#(3 - 16)m + 104 = 13#

#-13m + 104 = 13#

#-13m + 104 - color(red)(104) = 13 - color(red)(104)#

#-13m + 0 = --91#

#-13m = --91#

#(-13m)/color(red)(-13) = (-91)/color(red)(-13)#

#(color(red)(cancel(color(black)(-13)))m)/cancel(color(red)(-13)) = 7#

#m = 7#

Step 3: Substitute #7# for #m# in the solution to the first equation at the end of Step 1 and calculate #n#:

#n = 2m - 13# becomes:

#n = (2 xx 7) - 13#

#n = 14 - 13#

#n = 1#

The Solution Is: #m = 7# and #n = 1#