Tell whether each equation has one, zero, or infinitely many solutions. Solve the equation if it has one solution.

3(y - 2) = 3y - 6 PL HELPPP

3(y - 2) = 3y - 6

3y - 6 = 3y - 6

3y - 3y = - 6 + 6

0 = 0

It has ∞ solutions.

0 = 0, so 'y' can be replaced with any value & we'll still get the LHS & RHS as 0. So, the equation has ∞ solutions.

Hope it helps ⚜

Infinitely Many Solutions

Step-by-step explanation:

3(y - 2) = 3y - 6

3y - 6 = 3y - 6      Distribute 3.

0 = 0                    Combine the like terms.

Since we get the end result of 0 = 0, which is a true mathematical statement (i.e. 0 is equal to 0), we can see that regardless of the value of x, the original equation is true. So we have infinitely many equations.

Or, we can see the 2 parts as equations for 2 separate graphs. In other words, assume that we have 2 lines: y = (3x - 2) and y = 3y - 6. Since they both have the same m value (slope) and b value (y-intercept), the 2 lines are actually overlapping. So we have infinitely many solutions because the 2 equations represent the same linear graph.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this