Answers:
(0, 8)
(3, 6)
(6, 4)
(12, 0)
There are infinitely many answers to pick from. All that matters is that they are on the line 4x+6y = 48
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Explanation:
Plug in x = 0 and solve for y to get y = 8. That means we can have 0 cars and 8 vans.
Plug in y = 0 and solve for x to get x = 12. So we could have 12 cars and 0 vans.
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That takes care of two possible solutions, but we need 2 more.
Here's how to get more solutions. Start at the point (0,8). Then we'll use the slope to help get to another point. The slope here is -4/6 = -2/3, so we go down 2 and over to the right 3.
Starting at (0,8) and going down 2 and to the right 3 has us land on (3,6) which is another solution. I'll let you confirm if (x,y) = (3,6) works in the equation or not. This solution tells us we could have 3 cars and 6 vans.
Then from (3,6) we do another "down 2, right 3" motion to land on (6,4) which is yet another solution. In this case, we have 6 cars and 4 vans.
We can stop here since we have four solutions now.
