<PRE><B>Question 243708</B>
With the substitution method, you isolate one unknown and then substitute it into the other equation to find a solution. The equations are:
EQ1:  4m + n = 23
EQ2:  m - 4n= 10
.
Working with EQ2.
Add 4n to both sides.
m = 4n + 10
.
Now we can substitute it back into EQ1.
4(4n+10) + n = 23
Multiply through the left-hand pararentheses
16n + 40 + n = 23
Collect like terms
17n + 40 = 23
Subtract 40 from both sides
17n = - 17
Divide both sides by 17
n = -1
.
Now we take that value and substitute back into EQ2.
m = 4(-1) + 10
m = 6
.
So our proposed solution is:
n = -1
m = 6
.
We can check by putting these values back into the equations.
4(6) + (-1) = 24 - 1 = 23.  Check.
6 - 4(-1) = 6 + 4 = 10.  Check.</PRE>