solve by the substitution method. 2m+n=1 m-9n=10

To solve the system of equations using the substitution method, you need to isolate one variable in one equation and substitute it into the other equation. Here's how you can solve the equations 2m + n = 1 and m - 9n = 10 using this method:

Step 1: Solve one equation for one variable.
Let's solve the second equation, m - 9n = 10, for m:
m = 10 + 9n

Step 2: Substitute the expression for one variable into the other equation.
Replace m in the first equation, 2m + n = 1, with the expression we found in step 1:
2(10 + 9n) + n = 1

Step 3: Simplify the equation.
Distribute the 2 to the terms in parentheses:
20 + 18n + n = 1

Combine like terms:
19n + 20 = 1

Step 4: Solve for the remaining variable.
Move 20 to the right side by subtracting it from both sides:
19n = 1 - 20
19n = -19

Divide both sides by 19 to solve for n:
n = -19 / 19
n = -1

Step 5: Substitute the value of n back into one of the original equations to solve for the other variable.
Let's substitute n = -1 into the second equation, m - 9n = 10:
m - 9(-1) = 10
m + 9 = 10

Subtract 9 from both sides:
m = 10 - 9
m = 1

Therefore, the solution to the system of equations 2m + n = 1 and m - 9n = 10 is m = 1 and n = -1.