Question

Which statement describes the solution to the system of equations?

{2h+8k=6 and -5h-20k=-15 The system has exactly one solution. The system has exactly two solutions. The system has no solutions. The system has infinitely many solutions.

Answer 1

The given system of equations is two coincident lines since one equation is a multiple of the other, resulting in infinitely many solutions.

Step-by-step explanation:

The system of equations given is:

• 2h + 8k = 6
• -5h - 20k = -15

To determine the type of solution the system has, we can compare the coefficients of the variables. We notice that the second equation is -2.5 times the first equation. This means that they are essentially the same line, and therefore, the system does not have one single unique solution, but rather, these lines are coincident, leading us to conclude that there are infinitely many solutions to this system of equations.