Answer:
x = 3 and y = -4
Step-by-step explanation:
To solve the given system of equations by letting 1/x = M and 1/y = N, we can follow these steps:
1. Rewrite the system of equations using the variables M and N:
- 12M - 12N = 7
- 3M + 4N = 0
2. Solve one of the equations for M or N. Let's solve the second equation for M:
- 3M = -4N
- M = -4N/3
3. Substitute the value of M into the first equation:
- 12(-4N/3) - 12N = 7
- -48N/3 - 12N = 7
- -16N - 12N = 7
- -28N = 7
- N = 7/(-28)
- N = -1/4
4. Substitute the value of N into the equation we solved for M:
- M = -4(-1/4)/3
- M = 1/3
5. Determine the values of x and y using the values of M and N:
- 1/x = M
- 1/x = 1/3
- x = 3
- 1/y = N
- 1/y = -1/4
- y = -4
Therefore, the solution to the given system of equations is x = 3 and y = -4.
