solve by the substitution method:
8m+n=47
m-5n=52
thank you
having trouble completing please show all work so I can learn better
from the 2nd ---> m = 52 + 5n
into the 1st:
8(52+5n) + n = 47
for that I got n = -9
put that back into
m = 52 + 5n
= 52 - 45
= 7
3x=52+5y
2x=-48-7y
To solve the given system of equations using the substitution method, we need to isolate one variable in terms of the other in one of the equations and substitute that expression into the other equation.
Let's solve the second equation for m:
m - 5n = 52
Adding 5n to both sides:
m = 52 + 5n
Now we substitute this expression for m in the first equation:
8m + n = 47
8(52 + 5n) + n = 47
Simplify the equation:
416 + 40n + n = 47
41n + n = 47 - 416
41n + n = -369
42n = -369
Divide both sides by 42:
n = -369/42
n ≈ -8.79 (rounded to two decimal places)
Now that we have the value of n, we can substitute it back into one of the original equations to find m. Let's use the second equation:
m - 5n = 52
m - 5(-8.79) = 52
m + 43.95 = 52
m = 52 - 43.95
m ≈ 8.05 (rounded to two decimal places)
Therefore, the solution to the system of equations is approximately m ≈ 8.05 and n ≈ -8.79.