Final answer:
The system of equations is consistent and dependent, meaning both equations represent the same line. Therefore, the system has infinitely many solutions and we cannot solve for specific values of x and y.
Step-by-step explanation:
The system of equations provided is:
- -5x + 2y = 5
- -10x + 4y = -10
To solve this system using the elimination method, follow these steps:
- Identify if the equations are multiples of each other.
- When you notice that one equation is a multiple of the other, like in this case, the second equation is exactly 2 times the first, you can derive that the system has infinitely many solutions or no solution.
- Compare the equations. If they are consistent and dependent, then they represent the same line, resulting in infinitely many solutions. If the ratios of the coefficients are equal, but the constants are not, then the lines are parallel and there is no solution.
In this case:
- The ratio of the coefficients of x (-10/-5) equals the ratio of the coefficients of y (4/2).
- The ratio of the constants (-10/5) also equals the ratios of x and y coefficients.
- Hence, the system represents the same line, and there is an infinite number of solutions.
The system does not have a unique solution, and we cannot solve for a specific value of x or y. Instead, we write the solution as all points (x, y) that satisfy either of the original equations.