Solve the system by graphing. Check your solution.
y = -x + 2
y = x + 6
To solve the system by graphing, we can start by plotting the two equations on the same graph.
The first equation is y = -x + 2. To plot this line, we can start by finding two points on the line.
When x = 0, y = -0 + 2 = 2. This gives us the point (0, 2).
When x = 3, y = -3 + 2 = -1. This gives us the point (3, -1).
Plotting these points and drawing a line through them, we get:
y = -x + 2
Next, we can graph the second equation y = x + 6.
When x = 0, y = 0 + 6 = 6. This gives us the point (0, 6).
When x = -3, y = -3 + 6 = 3. This gives us the point (-3, 3).
Plotting these points and drawing a line through them, we get:
y = x + 6
To find the solution, we can look for the point where the two lines intersect. From the graph, it looks like they intersect at the point (2, 8).
Now, let's check the solution by substituting the values of x and y back into both equations:
For the first equation:
y = -x + 2
8 = -(2) + 2
8 = -2 + 2
8 = 0
For the second equation:
y = x + 6
8 = (2) + 6
8 = 8
Both equations are satisfied when x = 2 and y = 8, so the solution is (2, 8).
Therefore, the solution to the system of equations is (2, 8).
Solve the system by graphing. Check your solution.
y = -x - 5
y = x - 3
To solve the system by graphing, we can start by plotting the two equations on the same graph.
The first equation is y = -x - 5. To plot this line, we can start by finding two points on the line.
When x = 0, y = -(0) - 5 = -5. This gives us the point (0, -5).
When x = 3, y = -(3) - 5 = -8. This gives us the point (3, -8).
Plotting these points and drawing a line through them, we get:
y = -x - 5
Next, we can graph the second equation y = x - 3.
When x = 0, y = 0 - 3 = -3. This gives us the point (0, -3).
When x = -3, y = -3 - 3 = -6. This gives us the point (-3, -6).
Plotting these points and drawing a line through them, we get:
y = x - 3
To find the solution, we can look for the point where the two lines intersect. From the graph, it looks like they intersect at the point (-2, -1).
Now, let's check the solution by substituting the values of x and y back into both equations:
For the first equation:
y = -x - 5
-1 = -(-2) - 5
-1 = 2 - 5
-1 = -3
For the second equation:
y = x - 3
-1 = (-2) - 3
-1 = -5
Both equations are not satisfied when x = -2 and y = -1.
Therefore, there is no solution to the system of equations.