#### Answer

The solution is $(3, 4)$.

#### Work Step by Step

We can use the substitution method for this problem because in the second equation, $y$ is already isolated. We can use the expression for $y$ to substitute into the first equation:
$$3x - 2(10 - 2x) = 1$$
Use the distributive property to simplify:
$$3x - (2)(10) - (2)(-2x) = 1$$
Multiply out the terms:
$$3x - 20 + 4x = 1$$
Group like terms:
$$(3x + 4x) - 20 = 1$$
Combine like terms:
$$7x - 20 = 1$$
Add $20$ to each side to isolate the variable to one side of the equation and the constant to the other:
$$7x = 21$$
Divide each side of the equation by $7$ to solve for $x$:
$$x = 3$$
Now that we have the value for $x$, we can substitute this value into the second equation to find $y$:
$$y = 10 - 2(3)$$
Divide first, according to order of operations:
$$y = 10 - 6$$
Subtract to solve for $y$:
$$y = 4$$
The solution is $(3, 4)$.