After solving a system of linear equations, how can you check your answer to determine whether it is correct? Demonstrate the process of checking an answer with an example.

Check the answer by substituting the values for x and y into both equations to see that both equations are satisfied. We shall be happy to see your example.

no i need a example to show how it works out and on for to post to see other students to solve.

To check if the solution to a system of linear equations is correct, you can substitute the values found for the variables back into the original equations and see if both sides of the equation equal each other at the same time.

Let's demonstrate this process with an example:
Consider the system of equations:
1) 2x + 3y = 7
2) x - 2y = 4

Suppose we have found the solution x = 2 and y = 1. To confirm if this solution is correct, we can substitute these values into the original equations and check if both sides of the equation are equal.

Substitution into equation 1:
2(2) + 3(1) = 4 + 3 = 7 (LHS = RHS)

Substitution into equation 2:
2 - 2(1) = 2 - 2 = 0 (LHS ≠ RHS)

Since the LHS and RHS of equation 2 are not equal, this means that the proposed solution x = 2 and y = 1 is not correct. Therefore, you should review your calculations and find the correct solution.

To check if a solution to a system of linear equations is correct, you can substitute the values of the variables into the original equations and verify that both sides of each equation are equal.

Let's consider an example to illustrate this process:

Suppose we have the following system of linear equations:
1) 2x + y = 7
2) 3x - 2y = 4

To check if a potential solution, let's say x = 1 and y = 3, is correct, we substitute these values into the original equations:

1) 2(1) + 3 = 7
Simplifying, we get: 2 + 3 = 7
Thus, the left side of the equation equals the right side, as 5 = 7 is not true. Therefore, this equation is false.

2) 3(1) - 2(3) = 4
Simplifying, we get: 3 - 6 = 4
Again, the left side does not equal the right side as -3 = 4 is not true. Therefore, this equation is also false.

Since both equations do not hold true, this means that the values x = 1 and y = 3 do not solve the system of equations. Thus, this is not the correct solution.

By substituting the values of the variables into the original equations and ensuring that both sides are equal, you can confirm the accuracy of your solution to a system of linear equations. If the equations hold true, then you have found the correct solution. However, if even one equation does not hold true, then your answer is incorrect.