Question

Luca and William are playing a video game and they have scored a total of 20,000 points. Luca scored 8,000 more points than William. If you let l= the number of points that Luca scored, and w= the number of points that William scored, then the problem can be represented by the system:

l+w=20,000 and l=w+8,000

Graph the system. How many points did each boy score?

Answer 1

To solve this system, we can substitute the second equation into the first equation:

l = w + 8,000

Substitute l in the first equation:

w + 8,000 + w = 20,000
2w + 8,000 = 20,000
2w = 12,000
w = 6,000

Then, we can find l:

l = w + 8,000
l = 6,000 + 8,000
l = 14,000

So, Luca scored 14,000 points and William scored 6,000 points.

Now, we can graph the system:

The y-intercept is (0,20,000) and the x-intercept is (20,000,0)

The point where l=14,000 and w=6,000 is (14,000,6,000)

So, the graph would show a straight line connecting (0,20,000) and (20,000,0) with the point (14,000,6,000) marked on it.

Luca scored 14,000 points and William scored 6,000 points.