You are trying to guess the code to a puzzle while participating in an escape room. There are two buttons, blue and red, and you have to put the correct number in each one to unlock the door to the next room. There are only two clues to help you:Clue 1: If you double the blue number and add it to the red number, you get 6.Clue 2: If you quadruple the blue number and add it to double the red number, you get 12.You only get two attempts at the puzzle, and if you get it wrong, the game will be over. Use the system of equations shown to determine how many solutions there are to this puzzle.{2b+r=64b+2r=12 (1 point)ResponsesThere are only two solutions.There are only two solutions.There is only one solution.There is only one solution.There is no solution.There is no solution.There are infinitely many solutions. step by step bot

Answer 1

To solve this puzzle, we can set up a system of equations based on the given clues.

Let's define the variables:
b = blue number
r = red number

From clue 1, we have the equation:
2b + r = 6

From clue 2, we have the equation:
4b + 2r = 12

Now, we can solve this system of equations.

Step 1: Multiply the first equation by 2 to eliminate the variable r:
2(2b + r) = 2(6)
4b + 2r = 12

Step 2: Compare the result with the second equation:
4b + 2r = 12

Both equations are the same, which means they represent the same line. Therefore, there are infinitely many solutions to this puzzle.

Answer: There are infinitely many solutions.