Solve the system of equations by graphing. Then classify the system.
x+y=11
x-y=-5
graph the lines, see where they intersect. What is the question here?
To solve the system of equations by graphing, you can follow these steps:
1. Graph the first equation: x + y = 11
- To graph this equation, rearrange it to isolate y:
y = 11 - x
- Create a table of values by choosing different x values and plugging them into the equation to get corresponding y values.
- Plot the points on a graph and connect them to form a straight line.
2. Graph the second equation: x - y = -5
- Similarly, rearrange this equation to isolate y:
y = x + 5
- Choose different x values, calculate y, and plot the points on the graph.
3. Find the point where the two lines intersect.
- The point of intersection represents the solution to the system of equations.
4. Classify the system:
- If the two lines intersect at a single point, the system has a unique solution, and the equations are considered independent.
- If the two lines overlap (coincide), all points on the line are solutions to the system. These equations are essentially the same and are considered dependent.
- If the lines are parallel and do not intersect, there is no common solution, and the equations are inconsistent.
By following these steps, you can graph the system of equations, find the point of intersection, and classify the system based on the configuration of the lines.