Final answer:
The question pertains to solving a system of linear equations, which can be approached by substitution or elimination techniques to find the point where the two equations intersect graphically.
Step-by-step explanation:
Understanding Systems of Linear Equations
The question provided involves a system of linear equations, which is a set of two or more linear equations with the same variables. The solution to such a system is the point or points where the equations intersect on a graph. To solve a system of linear equations, one can use methods such as graphing, substitution, or elimination. Given the equations y = -½x + 4 and x + 2y = -8, the goal would be to find the values of x and y that satisfy both equations simultaneously.
To solve this particular system, one could use substitution or elimination. If substitution is chosen, you would solve one equation for one variable and then substitute that expression into the other equation. For elimination, you would add or subtract the equations to eliminate one of the variables, allowing you to find the value of the remaining variable.
For instance, by substituting y from the first equation into the second, you get x + 2(-½x + 4) = -8, which simplifies to x - x + 8 = -8. This would lead us to 0 = -16, indicating that there must be a mistake since this is a false statement. Alternatively, if using elimination, one might multiply the first equation by 2 to make the coefficients of y opposite numbers and then add the equations together to eliminate y.