Solve the system by graphing. Check your solution.
y = 2x
y = -2x + 8
To graph the system, we will plot the two equations on a coordinate plane:
First, let's graph the equation y = 2x:
For y = 2x:
- Pick any value for x and find the corresponding value of y.
- Repeat this process to get more points and plot them on the graph.
For example:
- When x = 0, y = 2(0) = 0. So we have the point (0,0).
- When x = 1, y = 2(1) = 2. So we have the point (1,2).
- When x = -1, y = 2(-1) = -2. So we have the point (-1,-2).
Plotting these points and drawing a line through them, we get a straight line passing through the origin with a positive slope.
Next, let's graph the equation y = -2x + 8:
For y = -2x + 8:
- Again, pick any value for x and find the corresponding value of y.
- Repeat this process to get more points and plot them on the graph.
For example:
- When x = 0, y = -2(0) + 8 = 8. So we have the point (0,8).
- When x = 1, y = -2(1) + 8 = 6. So we have the point (1,6).
- When x = -1, y = -2(-1) + 8 = 10. So we have the point (-1,10).
Plotting these points and drawing a line through them, we get a straight line with a negative slope that intersects the y-axis at (0,8).
After graphing both equations, we can determine the point where the two lines intersect. In this case, both lines intersect at (2,4).
To check our solution, substitute the x-coordinate (2) into either of the original equations:
For y = 2x, when x = 2, y = 2(2) = 4.
For y = -2x + 8, when x = 2, y = -2(2) + 8 = 4.
Since both equations give us the same y-coordinate (4) when x = 2, our solution is verified.
Therefore, the solution to the system of equations is (2,4).