1)

6m+n=47
m-4n=12

can someone help me solve using substitution method?

6m+n=47 --- (1)

m-4n=12 --- (2)

From (2),
m = 12 + 4n --- (3)

sub (3) into (1),
6(12 + 4n) + n = 47
72 + 24n + n = 47
25n = -25
n = -1

sub n = -1 into (3),
m = 12 + 4(-1)
m = 8

CHECK: sub m = 8 and n = -1 into (2),
8 - 4(-1) = 12

Sure! I'd be happy to help you solve the system of equations using the substitution method.

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. Let's start by solving one of the equations for one variable.

Let's solve the second equation, m - 4n = 12, for m:
m = 12 + 4n

Now we can substitute this expression for m in the first equation, 6m + n = 47:
6(12 + 4n) + n = 47

Expanding this equation, we get:
72 + 24n + n = 47

Combining like terms, we have:
25n + 72 = 47

Now, we can isolate the variable n by subtracting 72 from both sides:
25n = 47 - 72
25n = -25

Finally, we solve for n by dividing both sides by 25:
n = -25/25
n = -1

Now that we have found the value of n, we can substitute it back into the second equation to solve for m:
m - 4(-1) = 12
m + 4 = 12

Subtracting 4 from both sides, we get:
m = 12 - 4
m = 8

So the solution to the system of equations is m = 8 and n = -1.