Question

Given points p = (4x + 3, 5 + 2y) and q = (11, -5), find the values of x and y when p = q.

a) x = 2, y = -4
b) x = 1, y = -6
c) x = 3, y = -3
d) x = 4, y = -2

Answer 1

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:

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By solving these equations, we can find the values of x and y.

For the first equation:

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For the second equation:

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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.