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To solve the system of equations using the method of elimination, we can follow these steps:
1. Begin by writing down the two equations:
- 2x + 5y = 18
- 8x + 20y = 72
2. We need to make the coefficients of either x or y the same in both equations. In this case, let's focus on making the coefficients of y the same.
3. Multiply the first equation by 4 to match the coefficient of y:
- 8x + 20y = 72
- 8x + 20y = 72
4. Now, subtract the modified first equation from the second equation:
- (8x + 20y) - (8x + 20y) = 72 - 72
- 0 = 0
5. Since 0 = 0, this means that the system of equations is dependent. In this case, the equations represent the same line, so there are infinitely many solutions.
6. If we express the solution set in terms of y, it would be:
- y = any real number
- x = (18 - 5y) / 2
By following these steps, we can determine that the system of equations is dependent with infinitely many solutions. The solution set can be expressed in terms of y, with x being dependent on the value chosen for y.
