Question

2
which of the following best describes the solution to the system of equations below?

3x + 6y = 10
9x + 18y = 30

a. the system of equations has exactly one solution where x = 1 and y = 3/2.

b. the system of equations has exactly one solution where x = 10/3 and y = 0.

c. the system of equations has infinitely many solutions.

d. the system of equations has no solution.

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Explanation:

Step1: Simplify the second equation

Divide the second equation $9x + 18y = 30$ by 3: $3x + 6y = 10$.

Step2: Compare the two equations

The simplified second equation is identical to the first equation $3x + 6y = 10$, so they represent the same line.

Step3: Determine the number of solutions

Two identical lines intersect at infinitely many points, meaning infinitely many solutions.

Answer:

C. The system of equations has infinitely many solutions.