Solve the following system of equations by graphing. If the system is inconsistent or the equations are​ dependent, say so.

Question

7x-5y=2

14x-10y=4

Answer 1

Given System of Equations:

1. 7x - 5y = 2

2. 14x - 10y = 4

 

Analysis:

By multiplying the first equation by 2, we obtain:

2(7x - 5y) = 2 × 2, which simplifies to 14x - 10y = 4.

This is exactly the same as the second equation, indicating that the two lines represented by these equations are the same.

 

Conclusion:

The system of equations is dependent and not inconsistent. It has infinitely many solutions, as every solution of one equation is also a solution of the other.