Step-by-step explanation:
This system is independent because the graphs of the equations produce two different lines. If the equations produce the same line, they're dependent.
On the graph, the solution is found by locating the point of intersection, which is (2, 3). This point represents the values of x and y that satisfy both equations. We can check to make sure that they satisfy both equations by substituting the values into each equation.
For the first equation, we get 3 = -2 + 5, which is a true equation because -2 + 5 is equal to 3. This tells us that our solution satisfies the first equation. For the second equation, we get 3 = (1/2)(2) + 2, which is also a true equation. Since our solution satisfies both equations, we know that it is correct.
Example of an Algebraic Equation
When equations are graphed, we can quickly determine if a system is independent or not. We can also tell by examining the equations, as long as we know what to look for. In order for the system to be independent, the equations must have different lines when they are graphed. If the equations have different slopes and/or intercepts, they will create different lines. For our next example, we will identify the slope and intercept of each equation in a system of equations.
