Question

Tell whether each equation has one, zero, or infinitely many solutions.

Solve the equation if it has one solution.



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

Answer 1

Infinitely Many Solutions

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.

Answer 2

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.

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Hope it helps ⚜