Solve the system by graphing. Check your solution.
y=4x
y=-4x+8
To graph the system, we will plot the lines represented by each equation and see where they intersect.
First, let's graph y=4x:
Plotting a few points, we have:
When x=0, y=4(0)=0. So, the point (0,0) is on the line.
When x=1, y=4(1)=4. So, the point (1,4) is on the line.
When x=-1, y=4(-1)=-4. So, the point (-1,-4) is on the line.
Connecting these points, we get a straight line that passes through (0,0), (1,4), and (-1,-4).
Next, let's graph y=-4x+8:
Plotting a few points, we have:
When x=0, y=-4(0)+8=8. So, the point (0,8) is on the line.
When x=1, y=-4(1)+8=4. So, the point (1,4) is on the line.
When x=-1, y=-4(-1)+8=12. So, the point (-1,12) is on the line.
Connecting these points, we get a straight line that passes through (0,8), (1,4), and (-1,12).
Now, let's check the solution by looking at where the lines intersect:
From the graph, we can see that the lines intersect at the point (1,4).
Now let's substitute this solution into the original equations:
For y=4x:
4(1)=4, which is true.
For y=-4x+8:
-4(1)+8=4, which is also true.
Since the solution satisfies both equations, we can conclude that the solution is (1,4).
Therefore, the system is solved by graphing, and the solution is checked to be correct.