Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.

x + 10y = 41
x + 9y = 37

x = 37 - 9y

x + 10y = 41

Substitute 37-9y for x in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.

To solve this system of equations using the substitution method, we'll start by solving one of the equations for one variable and then substituting it into the other equation.

Let's solve the second equation for x:
x + 9y = 37
x = 37 - 9y

Now we substitute this expression for x in the first equation:
x + 10y = 41
(37 - 9y) + 10y = 41
37 - 9y + 10y = 41
37 + y = 41

Simplifying further:
y = 41 - 37
y = 4

Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the second equation:
x + 9y = 37
x + 9(4) = 37
x + 36 = 37
x = 37 - 36
x = 1

Therefore, the solution to the system of equations is x = 1 and y = 4.

We can verify this solution by substituting these values into both original equations. If the left side equals the right side in both equations, we have found the correct solution.