Mya and Liliana are analyzing a system of equations, 2x−5=6y and y=1/3x+4. Mya says there is no solution and Liliana says there are an infinite number of solutions. Which options best explains what is going on?

Answer 1

The two equations given are 2x−5=6y and y=1/3x+4. We can solve this system of equations to determine if there is a solution or if there are an infinite number of solutions.

To find the solution, we can substitute the value of y from the second equation into the first equation:

2x−5=6(1/3x+4)
2x−5=2x+24

Rearranging the equation, we have:

2x - 2x = 24 + 5
0 = 29

This equation is false since 0 is not equal to 29. Therefore, the system of equations has no solution.

Hence, Mya is correct in stating that there is no solution.