SOLUTION: 4m + n =2 m - 8n =50 solve by using the substitution method. what is the solution of the system?

Question 549726: 4m + n =2
m - 8n =50
solve by using the substitution method. what is the solution of the system?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equations are:
4m + n = 2 (equation 1)
m - 8n = 50 (equation 2)
solve for m in equation 2 to get:
m = 8n + 50 (equation 3)
substitute for m in equation 1 to get:
4(8n+50) + n = 2 which becomes:
32n + 200 + n = 2 which becomes:
33n + 200 = 2
subtract 200 from both sides of this equation to get:
33n = -198
divide both sides of this equation by 33 to get:
n = -6
now that you know the value of n, you can go back and solve for m in equation 3.
equation 3 becomes:
m = 8(-6) + 50) which becomes:
m = -48 + 50 which becomes:
m = 2
now you have values for m and n and you can go back to the original equations to confirm that you got the right values.
if you did, using those values will solve both equations simultaneously.
your values are:
n = -6
m = 2
original equations are:
4m + n = 2 (equation 1)
m - 8n = 50 (equation 2)
substituting 2 for m and -6 for n gets you:
4(2) + (-6) = 2 (equation 1)
(2) - 8(-6) = 50 (equation 2)
this results in:
8 - 6 = 2 (equation 1)
2 + 48 = 50(equation 2)
since both equations are true (the left side of each equations equals the right side of each equation), then the values you solved for are good.

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