Final answer:
To solve the equation x + 2y = 12 algebraically, rearrange the equation and solve for one variable, then substitute that value into the other equation. The solution to the equation is x = 4 and y = 4.
Step-by-step explanation:
To solve the equation x + 2y = 12 algebraically, we need to eliminate one variable in order to isolate the other variable. We can do this by rearranging the equation to solve for one variable and substituting that into the other equation. Let's solve for y first:
x + 2y = 12
y = (12 - x) / 2
Now that we have an expression for y, we can substitute it into the other equation:
y = 2x - 4
(12 - x) / 2 = 2x - 4
Simplifying this equation, we get:
12 - x = 4x - 8
Now, we can solve for x:
12 + 8 = 4x + x
20 = 5x
x = 4
To find y, we can substitute x = 4 into either of the original equations:
y = (12 - 4) / 2
y = 8 / 2
y = 4
Therefore, the solution to the equation is x = 4 and y = 4.