Final answer:
The student's problem is to find values for x and y given points p and q. By setting the components of p equal to those of q, we determined that the values should be x = 2 and y = -5, which does not match any of the provided options.
Step-by-step explanation:
The student is asking to find values for variables x and y such that the point p will be equal to point q, given that p = (4x + 3, 5 + 2y) and q = (11, -5). To solve this problem, we need to set the corresponding components of points p and q equal to each other. This gives us two equations:
By solving these equations, we can find the values of x and y.
For the first equation:
For the second equation:
However, after solving these equations, we see that y should actually be -5, not -4 as suggested in option (a), thus there appears to be an inconsistency, suggesting a possible error in the given options or a typo. The correct values of x and y, based on solving the equations, should be x = 2 and y = -5.