SOLUTION: Can you help me solve: 5m+n=8 3m-4n=14

Algebra ->  Expressions-with-variables -> SOLUTION: Can you help me solve: 5m+n=8 3m-4n=14      Log On


   

Question 134807This question is from textbook Algebra 1
: Can you help me solve:
5m+n=8
3m-4n=14 This question is from textbook Algebra 1

Found 2 solutions by vleith, algebrapro18:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve by substitution
Given : 5m+%2B+n+=+8 and 3m+-4n+=+14
5m+%2B+n+=+8
+n+=+8+-+5m
Now use that value of n and sub back into the second equation
3m+-4n+=+14
3m+-+4%288+-+5m%29+=+14
3m+-32+%2B+20m+=+14
23m+=+46+
+m+=+2
Use this value of m any equation to find n
n+=+8+-+5%282%29
n+=+-2
verify the answer
Does 3%2A%282%29+-4%2A%28-2%29+=+14 ???
+6+%2B+8+=+14+ check!

Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
For this system of equations it would be best to solve it using substitution. The steps for substitution are:

1) Solve one of the equations for one of the variables.
2) Plug the value from 1 into the other equation and solve for the remaining single variable.
3) Plug the value from 2 into the equation from 1 and solve for the remaining variable.

5m + n = 8
3m - 4n = 14

1. Solve 5m + n = 8 for n:

5m + n = 8
n = 8 - 5m

2. Plug n = 8 - 5m into 3m - 4n = 14 and solve for m.

3m - 4n = 14
3m - 4(8 - 5m) = 14
3m - 32 + 20m = 14
23m - 32 = 14
23m = 46
m = 2

3. Plug m = 2 into n = 8-5m and solve for n.

n = 8 - 5m
n = 8 - 5(2)
n = 8 - 10
n = -2

so your solutions are m = 2 and n = -2. Now to check our answers.

5m + n = 8
5(2) - 2 = 8
10 - 2 = 8
8 = 8

this equation checks out, now lets check the next one

3m - 4n = 14
3(2)- 4(-2) = 14
6 + 8 = 14
14 = 14

since both of these check out then we know our solutions are right.