When an equation has infinitely many solutions, it is the exact same equation on both sides. For example, for this to be infinitely many, it would have to be:
5c+9=5x+9
This would be infinitely many, because it would be the same line plotted twice, so it would have an infinite amount of intersecting points.
This also cannot be one solution, because they have the same slope. When an equation has the same slope, it can either be infinitely many solutions or one solution. We already explained why this is not infinitely many, but it is also not one solution. If plotted, these points could never intersect. For this to be one solution, it would have to be:
5c+9=4c-12
This means the equation has no solution. It will never intersect. Let’s prove this by solving:
5c+9=5c-12
*subtract 5c on both sides*
9=-12
Since this is not true and 9 does not equal -12, there is no solution
Hope this helps comment below for more questions :)
Step-by-step explanation: First, you would add + 12 to both sides of the equation so that you would have 5c + 21 = 5c. Then, you would subtract 5c from both sides of the equation. This would leave you with 21 = 0. Since this is not true, the equation would have no solution.
