Explicitly explain how to tell an answer is correct when solvingi systems of equations.
-thanks so much!
Substitute the answer you obtain for the variables and verify that all equations are satisfied.
When solving a system of equations, there are different methods you can use, such as substitution, elimination, or graphing. Once you have obtained a solution, you can verify its correctness by following these steps:
1. Substitute the values of the variables obtained in the solution back into the original equations. This ensures that the solution satisfies all the equations simultaneously.
2. Evaluate the left side and right side of each equation by plugging in the values of the variables. If both sides of each equation are equal, then the solution is correct.
3. Repeat this process for all the equations in the system. If the solution holds true for every equation, then it is indeed the correct solution.
For example, let's say we have the following system of equations:
Equation 1: 2x + 3y = 7
Equation 2: 4x - 2y = 10
If we solve this system and obtain the solution x = 2 and y = 1, we can then substitute these values back into the original equations:
Equation 1 (substituting x = 2 and y = 1): 2(2) + 3(1) = 4 + 3 = 7 (left side = right side)
Equation 2 (substituting x = 2 and y = 1): 4(2) - 2(1) = 8 - 2 = 6 (left side ≠ right side)
Since Equation 2 does not hold true for the obtained solution, x = 2 and y = 1, we conclude that this solution is incorrect. Therefore, it is necessary to revise the solution and re-check its validity using the steps mentioned above.