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.

Question

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.

Answer 1

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.

Answer 2

To solve this puzzle, we can create a system of equations based on the given clues. Let's assign the blue number as "b" and the red number as "r".

From Clue 1: "If you double the blue number and add it to the red number, you get 6", we can write the equation: 2b + r = 6.

From Clue 2: "If you quadruple the blue number and add it to double the red number, you get 12", we can write the equation: 4b + 2r = 12.

Now, we have the following system of equations:

Equation 1: 2b + r = 6
Equation 2: 4b + 2r = 12

To determine the number of solutions to this system, we need to solve it. We can do this by using either substitution or elimination.

Let's solve it using elimination:

Multiply Equation 1 by 2 to make the coefficients of "r" in both equations equal:
2*(2b + r) = 2*6
4b + 2r = 12

Now we have two identical equations:
4b + 2r = 12

Since both equations are identical, they represent the same line. This means that the system has infinitely many solutions. Hence, the correct response is:

There are infinitely many solutions.

Answer 3

To solve the system of equations, we can use the method of substitution:

First starting with equation 1: 2b + r = 6

We can isolate r by subtracting 2b from both sides:
r = 6 - 2b

Now we substitute this value of r into equation 2: 64b + 2r = 12
64b + 2(6 - 2b) = 12

Simplifying the equation:
64b + 12 - 4b = 12
60b = 0

Dividing both sides by 60:
b = 0

Now we substitute this value of b into equation 1: 2b + r = 6
2(0) + r = 6
r = 6

So the values for b and r are both 0.

Therefore, there is only one solution to this puzzle.