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A system of equations has an infinite number of solutions.3y−4x=53𝑦−4𝑥=53y+bx=c3𝑦+𝑏𝑥=𝑐What are the values of b𝑏 and c𝑐?Enter your answer in the boxes.

Question

A system of equations has an infinite number of solutions.3y−4x=53𝑦−4𝑥=53y+bx=c3𝑦+𝑏𝑥=𝑐What are the values of b𝑏 and c𝑐?Enter your answer in the boxes.

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Solution

The system of equations given is:

  1. 3y - 4x = 5
  2. 3y + bx = c

For the system to have an infinite number of solutions, the two equations must represent the same line. This means the coefficients of x and y in both equations must be the same.

From the first equation, the coefficient of y is 3 and the coefficient of x is -4.

So, for the second equation to represent the same line, the coefficient of y must also be 3 and the coefficient of x must also be -4. This means b = -4.

Substituting y = (5 + 4x) / 3 into the second equation gives:

3((5 + 4x) / 3) - 4x = c 5 - 4x = c

So, c = 5.

Therefore, the values of b and c that make the system have an infinite number of solutions are b = -4 and c = 5.

This problem has been solved

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