Describe the number of solutions for the equation.
13.
3(x – 3) = 3x (1 point)
one solution
no solution
infinitely many solutions
14.
–2(y – 3) = 2y – 6 (1 point)
one solution
no solution
infinitely many solutions
3x-3 = 3x
no solutions
-2y+6 = 2y-6
one solution
To determine the number of solutions for each equation, we can solve them by simplifying and rearranging the equation to isolate the variable.
For the first equation, 3(x – 3) = 3x, we can begin by distributing the 3 on the left side of the equation:
3x - 9 = 3x
Next, we can subtract 3x from both sides to eliminate the variable terms:
-9 = 0
The equation simplifies to -9 = 0, which is a contradiction since -9 is not equal to 0. Therefore, there are no solutions to this equation.
For the second equation, -2(y – 3) = 2y – 6, we start by distributing -2 on the left side:
-2y + 6 = 2y - 6
Then, we can combine like terms by adding 2y to both sides:
6 = 4y - 6
Next, we add 6 to both sides:
12 = 4y
Finally, we divide both sides by 4 to isolate the variable:
3 = y
Since we were able to find a specific value for y, there is exactly one solution to this equation.
Therefore, the answer for question 13 is "no solution," and the answer for question 14 is "one solution."