Find the values of p and q for which the following system has infinitely many solutions:2x + 3y = 7   (p + q)x + (2p – q)y = 21.p = 4, q = 3p = l, q = 5p = 5, q = lp = 3, q = 4

For a system of linear equations to have infinitely many solutions, the two equations must be proportional to each other. This means that the coefficients of the variables in one equation must be a constant multiple of the coefficients of the variables in the other equation.

The given system of equations is:

1. 2x + 3y = 7
2. (p + q)x + (2p – q)y = 21

We can write the second equation as:

2. px + qx + 2py - qy = 21

For the system to have infinitely many solutions, the coefficients of x and y in the first equation must be equal to the coefficients of x and y in the second equation. Therefore, we have:

p + q = 2 (equation 3) 2p - q = 3 (equation 4)

We can solve this system of equations to find the values of p and q.

Adding equation 3 and equation 4 gives:

3p = 5 => p = 5/3

Substituting p = 5/3 into equation 3 gives:

5/3 + q = 2 => q = 2 - 5/3 => q = 1/3

So, the values of p and q for which the given system has infinitely many solutions are p = 5/3 and q = 1/3. None of the given options match these values.