Question

Identify which equations have one solution, infinitely many solutions, or no solution.

Answer 1

Here’s what I found online ...

Let's label them 1-6, for convenience.
1. 1 solution (a positive # of ys equaling a positive constant)
2. Infinitely many solutions (You get 0=0 if you completely simplify)
3. No solution (take out the 3z's; 2.5 doesn't equal 3.2)
4. Infinitely many solutions (take out the 3/4 x; 1.1+2 = 3.1)
5. No solution (take out the 4.5r; 0 doesn't equal 3.2)
6. 1 solution (x = 3 1/2)

Other than that, what are the equations? Do you have an attachment?

Answer 2

Having one solution, infinitely many solutions or no solution. These are called "Simultaneous Equations" or "Systems of Equation". They are for if you want to find the intercepts of both graphs.

Having only one solution, meaning that both graphs intercept each others at only one single ordered pair or only a single (x,y).

Having infinite many solutions, meaning that both graphs are same and intercept infinitely (For example if you have to solve 2 quadratic equations and find the intercepts. Given that both quadratic equations are the same equations. For example, x^2 = x^2 as you'll get x^2-x^2 = 0, 0=0. Notice that when it's 0=0. That means the equation is true for all real numbers (Because x^2 = x^2 which is always true.)

Having no solution, meaning that the graph doesn't intersect another graph. When you do the equations, you might expect something like 2 = 0. For example,

$x+1=x+6\\x+1-x-6=0\\0-5=0\\0=5$

Notice how 0 = 5 is false. If the equation is false, that means the equation is not true for all real numbers. So no matter what x values you are going to substitute in, it won't be true (considering both graphs don't intercept each others.)