Question

How many solutions does this system of equations have?
x/4 + y/9 = 27
3x/2 + 2y/3 = 19

Answer 1

The system of equations has no solution.

Step-by-step explanation:

To determine the number of solutions in the given system of equations:

x/4 + y/9 = 27

3x/2 + 2y/3 = 19

1. Multiply the first equation by the least common multiple (LCM) of the denominators, which is 36, to eliminate the fractions. This gives you 9x + 4y = 972.
2. Multiply the second equation by the LCM of the denominators, which is 6, to eliminate the fractions. This gives you 9x + 4y = 114.
3. Comparing the two equations, we can see that the left sides are equal, but the right sides are different. This means that the system of equations is inconsistent and has no solution.