Answer:
1. One solution
2. Infinite solutions
3. No solutions
Explanation:
To determine if a system has infinite solutions or no solutions, we need to look at 2 very important things: slope and the y - int.
If a line has both the slope and the y-int the same, that means that they are the same line--and are on top of each other, therefore meaning that there will be infinite solutions.
If a line has the same slope and a different y-int, this means that there are no solutions. The slope is the same and y-int different, meaning they're parallel lines.
If a line has a different slope and the same y-int, then it has one solution, and if a line has a different slope and a different y-int, they also have one solution.
Let's look at the first question. We can see it is in slope-intercept form, giving us the slope and the y-int. The slope for the first equation is 7 and the y-int is 0, and for the second, the slope is 3, and the y-int is -3. Since both the slope and the y-int are different, there is one solution.
In the next problem, however, we see that the slopes for both equations are 8, and the y-ints are also both 0. This signifies that they are on the same line and that they have infinite solutions.
Lastly, the third problem has the same slope for each of 3/2, but the second has a different y-int, 4 rather than 0. Because they have the same slope but a different y-int, they are parallel and have no solutions.
Hope this helps!