To solve this system of equations, we can use the method of substitution.
From the first equation, we have: 2b + r = 6
Rearranging the equation, we get: r = 6 - 2b
Substituting this expression for r into the second equation, we have: 4b + 2(6 - 2b) = 12
Expanding and simplifying, we get: 4b + 12 - 4b = 12
Simplifying further, we have: 12 = 12
This equation implies that 12 equals 12, which is true. Because this is a true statement, it means that there is no restriction on the value of b. Therefore, there are infinitely many solutions to this puzzle, as any value of b can be chosen.
So, the correct answer is: There are infinitely many solutions.
ou 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) Responses There is no solution. There is no solution. There are only two solutions. There are only two solutions. There is only one solution. There is only one solution. There are infinitely many solutions. There are infinitely many solutions.
1 answer