Final answer:
To solve the system of equations using substitution, solve one equation for one variable in terms of the other variable. Substitute the expression for the variable into the other equation and solve for the remaining variable. The solution to the system of equations is x = 3 and y = 2 (A).
Step-by-step explanation:
To solve this system of equations using substitution, we can start by solving one equation for one variable in terms of the other variable. We can choose to solve the first equation, y = 2x - 4, for y in terms of x. By substituting this expression for y into the second equation, x + 2y = 10, we can find the value of x.
Now let's solve the first equation, y = 2x - 4, for y:
Substituting 2x - 4 for y in the second equation, x + 2(2x - 4) = 10:
Simplifying the equation: x + 4x - 8 = 10, gives us 5x - 8 = 10
Solving for x, we have 5x = 18, which means x = 3.
Substituting this value of x into the first equation, y = 2(3) - 4, we find y = 2.
Therefore, the solution to the system of equations is x = 3 and y = 2. So, the correct answer is a. x = 3, y = 2 (A).